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Understanding and Solving Conic Sections: A Student's Guide with Examples

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Gabriella Mulé

@bellamule08

Analytical geometry bridges algebra and geometry, letting you solve geometric... Show more

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Introduction to Analytical Geometry analytical geometry- analysis of geometry using algebraic methods. We mainly analyze conic sections All

Introduction to Analytical Geometry

Analytical geometry uses algebraic methods to analyze geometric shapes. The star players here are conic sections, all derived from the second-degree equation: Ax2+Bxy+Cy2+Dx+Ey+F=0Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.

When working with circles, the standard equation is (x−h)2+(y−k)2=r2(x-h)^2 + (y-k)^2 = r^2, where (h,k)(h,k) is the center and rr is the radius. For example, if you have x2+y2−6x+4y+7=0x^2 + y^2 - 6x + 4y + 7 = 0, you can rearrange it to (x−3)2+(y+2)2=6(x - 3)^2 + (y + 2)^2 = 6, revealing a circle with center at (3,−2)(3, -2) and radius 6\sqrt{6}.

To find intersections between lines and circles, substitute the line equation into the circle equation. For instance, finding where y=2x−2y = 2x - 2 meets x2+y2=25x^2 + y^2 = 25 involves substituting the yy value, solving the resulting quadratic, and finding the corresponding points: (3,4)(3, 4) and (75,−245)(\frac{7}{5}, \frac{-24}{5}).

💡 Quick Tip: When working with circle equations, always try to get them into standard form (x−h)2+(y−k)2=r2(x-h)^2 + (y-k)^2 = r^2 by completing the square for both xx and yy terms. This makes identifying the center and radius immediate!

An ellipse is a set of points where the sum of distances from any point on the ellipse to two fixed points (called foci) remains constant. The standard equation for an ellipse centered at the origin is x2a2+y2b2=1\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, where aa and bb control the ellipse's size and shape.

Introduction to Analytical Geometry analytical geometry- analysis of geometry using algebraic methods. We mainly analyze conic sections All

Ellipses and Hyperbolas

For an ellipse with center at (h,k)(h,k), the equation becomes (x−h)2a2+(y−k)2b2=1\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1. The vertices are found at (h±a,k)(h±a, k) and (h,k±b)(h, k±b). The foci depend on whether the ellipse is horizontal $(h±c, k)$ where $c^2 = a^2 - b^2$ or vertical $(h, k±c)$ where $c^2 = b^2 - a^2$.

When analyzing an ellipse like 4x2+9y2−16x+18y−11=04x^2 + 9y^2 - 16x + 18y - 11 = 0, rearrange it into standard form by completing the square. The result, (x−2)29+(y+1)24=1\frac{(x - 2)^2}{9} + \frac{(y + 1)^2}{4} = 1, reveals a center at (2,−1)(2,-1) with a=3a=3 and b=2b=2. From here, you can find vertices at (5,−1)(5,-1), (−1,−1)(-1,-1), (2,1)(2,1), and (2,−3)(2,-3), and foci at (2±5,−1)(2 ± \sqrt{5},-1).

A hyperbola is defined by the constant difference between distances from any point to two fixed points. For a hyperbola centered at the origin, the equation is x2a2−y2b2=1\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 (horizontal) or y2b2−x2a2=1\frac{y^2}{b^2} - \frac{x^2}{a^2} = 1 (vertical).

🔑 Remember: In both ellipses and hyperbolas, aa and bb determine the shape, but for hyperbolas, the relationship between aa, bb, and cc is c2=a2+b2c^2 = a^2 + b^2 unlike ellipses where $c^2 = |a^2 - b^2|$.

Introduction to Analytical Geometry analytical geometry- analysis of geometry using algebraic methods. We mainly analyze conic sections All

Hyperbolas and Their Asymptotes

Hyperbolas have special lines called asymptotes that the curve approaches but never touches. For a hyperbola centered at the origin, these asymptotes follow the equation y=±baxy = ±\frac{b}{a}x. For hyperbolas centered at (h,k)(h,k), the asymptotes become y−k=±ba(x−h)y - k = ±\frac{b}{a}(x - h).

When graphing hyperbolas, follow this process: plot the center, mark the vertices, construct a rectangle using the vertices, and extend the rectangle's diagonals to create the asymptotes. The hyperbola's curves will approach these asymptotes but never cross them.

For a hyperbola like 4x2−9y2+16x−18y−29=04x^2 - 9y^2 + 16x - 18y - 29 = 0, complete the square to get (x+2)29−(y+1)24=1\frac{(x + 2)^2}{9} - \frac{(y + 1)^2}{4} = 1. This reveals a horizontal hyperbola with center at (−2,−1)(-2,-1), where a=3a=3 and b=2b=2. The foci are at (−2±13,−1)(-2±\sqrt{13},-1) since c2=a2+b2=13c^2 = a^2 + b^2 = 13.

🚀 Visualization Trick: Think of hyperbolas as two separate curves that mirror each other across the center. The asymptotes form an "X" that guides where the curves will go as they extend outward.

A parabola is the set of points where the distance from a fixed point (the focus) equals the distance to a fixed line (the directrix). The standard form varies depending on whether the parabola opens vertically or horizontally.

Introduction to Analytical Geometry analytical geometry- analysis of geometry using algebraic methods. We mainly analyze conic sections All

Parabolas

Vertical parabolas have the equation y=14p(x−h)2+ky = \frac{1}{4p}(x-h)^2 + k (where $x$ is squared), with vertex at (h,k)(h,k), focus at (h,k+p)(h,k+p), and directrix at y=k−py=k-p. These parabolas open upward or downward.

Horizontal parabolas follow x=14p(y−k)2+hx = \frac{1}{4p}(y-k)^2 + h (where $y$ is squared), with vertex at (h,k)(h,k), focus at (h+p,k)(h+p,k), and directrix at x=h−px=h-p. These parabolas open right or left.

When analyzing parabolas like 4y2+2x−16y+13=04y^2+2x-16y+13=0, rearrange the equation by completing the square. For this example, you get −2(y−2)2+1.5=x-2(y-2)^2+1.5=x which is a horizontal parabola with vertex at (1.5,2)(1.5,2). The constant −2-2 equals 14p\frac{1}{4p}, so p=−0.125p=-0.125, placing the focus at (1.37,2)(1.37,2) and the directrix at x=1.625x=1.625.

🎯 Test Prep Tip: The key to solving conic section problems is identifying which type you're dealing with. Look at the squared terms! If both x2x^2 and y2y^2 have the same sign, it's a circle or ellipse. Different signs indicate a hyperbola. If only one variable is squared, it's a parabola.

The power of analytical geometry lies in transforming visual problems into equations you can solve systematically. Whether you're dealing with circles, ellipses, hyperbolas, or parabolas, the standard forms give you a clear roadmap to find key features like centers, vertices, foci, and directrices.



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What is the Knowunity AI companion?

Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.

Where can I download the Knowunity app?

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Is Knowunity really free of charge?

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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

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I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user

 

Algebra 2

•

64

•

Dec 5, 2025

•

4 pages

Understanding and Solving Conic Sections: A Student's Guide with Examples

user profile picture

Gabriella Mulé

@bellamule08

Analytical geometry bridges algebra and geometry, letting you solve geometric problems with equations. In this topic, you'll explore conic sections—circles, ellipses, hyperbolas, and parabolas—all derived from second-degree equations that create fascinating curves with real-world applications.

Introduction to Analytical Geometry analytical geometry- analysis of geometry using algebraic methods. We mainly analyze conic sections All

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Introduction to Analytical Geometry

Analytical geometry uses algebraic methods to analyze geometric shapes. The star players here are conic sections, all derived from the second-degree equation: Ax2+Bxy+Cy2+Dx+Ey+F=0Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.

When working with circles, the standard equation is (x−h)2+(y−k)2=r2(x-h)^2 + (y-k)^2 = r^2, where (h,k)(h,k) is the center and rr is the radius. For example, if you have x2+y2−6x+4y+7=0x^2 + y^2 - 6x + 4y + 7 = 0, you can rearrange it to (x−3)2+(y+2)2=6(x - 3)^2 + (y + 2)^2 = 6, revealing a circle with center at (3,−2)(3, -2) and radius 6\sqrt{6}.

To find intersections between lines and circles, substitute the line equation into the circle equation. For instance, finding where y=2x−2y = 2x - 2 meets x2+y2=25x^2 + y^2 = 25 involves substituting the yy value, solving the resulting quadratic, and finding the corresponding points: (3,4)(3, 4) and (75,−245)(\frac{7}{5}, \frac{-24}{5}).

💡 Quick Tip: When working with circle equations, always try to get them into standard form (x−h)2+(y−k)2=r2(x-h)^2 + (y-k)^2 = r^2 by completing the square for both xx and yy terms. This makes identifying the center and radius immediate!

An ellipse is a set of points where the sum of distances from any point on the ellipse to two fixed points (called foci) remains constant. The standard equation for an ellipse centered at the origin is x2a2+y2b2=1\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, where aa and bb control the ellipse's size and shape.

Introduction to Analytical Geometry analytical geometry- analysis of geometry using algebraic methods. We mainly analyze conic sections All

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Ellipses and Hyperbolas

For an ellipse with center at (h,k)(h,k), the equation becomes (x−h)2a2+(y−k)2b2=1\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1. The vertices are found at (h±a,k)(h±a, k) and (h,k±b)(h, k±b). The foci depend on whether the ellipse is horizontal $(h±c, k)$ where $c^2 = a^2 - b^2$ or vertical $(h, k±c)$ where $c^2 = b^2 - a^2$.

When analyzing an ellipse like 4x2+9y2−16x+18y−11=04x^2 + 9y^2 - 16x + 18y - 11 = 0, rearrange it into standard form by completing the square. The result, (x−2)29+(y+1)24=1\frac{(x - 2)^2}{9} + \frac{(y + 1)^2}{4} = 1, reveals a center at (2,−1)(2,-1) with a=3a=3 and b=2b=2. From here, you can find vertices at (5,−1)(5,-1), (−1,−1)(-1,-1), (2,1)(2,1), and (2,−3)(2,-3), and foci at (2±5,−1)(2 ± \sqrt{5},-1).

A hyperbola is defined by the constant difference between distances from any point to two fixed points. For a hyperbola centered at the origin, the equation is x2a2−y2b2=1\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 (horizontal) or y2b2−x2a2=1\frac{y^2}{b^2} - \frac{x^2}{a^2} = 1 (vertical).

🔑 Remember: In both ellipses and hyperbolas, aa and bb determine the shape, but for hyperbolas, the relationship between aa, bb, and cc is c2=a2+b2c^2 = a^2 + b^2 unlike ellipses where $c^2 = |a^2 - b^2|$.

Introduction to Analytical Geometry analytical geometry- analysis of geometry using algebraic methods. We mainly analyze conic sections All

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Hyperbolas and Their Asymptotes

Hyperbolas have special lines called asymptotes that the curve approaches but never touches. For a hyperbola centered at the origin, these asymptotes follow the equation y=±baxy = ±\frac{b}{a}x. For hyperbolas centered at (h,k)(h,k), the asymptotes become y−k=±ba(x−h)y - k = ±\frac{b}{a}(x - h).

When graphing hyperbolas, follow this process: plot the center, mark the vertices, construct a rectangle using the vertices, and extend the rectangle's diagonals to create the asymptotes. The hyperbola's curves will approach these asymptotes but never cross them.

For a hyperbola like 4x2−9y2+16x−18y−29=04x^2 - 9y^2 + 16x - 18y - 29 = 0, complete the square to get (x+2)29−(y+1)24=1\frac{(x + 2)^2}{9} - \frac{(y + 1)^2}{4} = 1. This reveals a horizontal hyperbola with center at (−2,−1)(-2,-1), where a=3a=3 and b=2b=2. The foci are at (−2±13,−1)(-2±\sqrt{13},-1) since c2=a2+b2=13c^2 = a^2 + b^2 = 13.

🚀 Visualization Trick: Think of hyperbolas as two separate curves that mirror each other across the center. The asymptotes form an "X" that guides where the curves will go as they extend outward.

A parabola is the set of points where the distance from a fixed point (the focus) equals the distance to a fixed line (the directrix). The standard form varies depending on whether the parabola opens vertically or horizontally.

Introduction to Analytical Geometry analytical geometry- analysis of geometry using algebraic methods. We mainly analyze conic sections All

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Parabolas

Vertical parabolas have the equation y=14p(x−h)2+ky = \frac{1}{4p}(x-h)^2 + k (where $x$ is squared), with vertex at (h,k)(h,k), focus at (h,k+p)(h,k+p), and directrix at y=k−py=k-p. These parabolas open upward or downward.

Horizontal parabolas follow x=14p(y−k)2+hx = \frac{1}{4p}(y-k)^2 + h (where $y$ is squared), with vertex at (h,k)(h,k), focus at (h+p,k)(h+p,k), and directrix at x=h−px=h-p. These parabolas open right or left.

When analyzing parabolas like 4y2+2x−16y+13=04y^2+2x-16y+13=0, rearrange the equation by completing the square. For this example, you get −2(y−2)2+1.5=x-2(y-2)^2+1.5=x which is a horizontal parabola with vertex at (1.5,2)(1.5,2). The constant −2-2 equals 14p\frac{1}{4p}, so p=−0.125p=-0.125, placing the focus at (1.37,2)(1.37,2) and the directrix at x=1.625x=1.625.

🎯 Test Prep Tip: The key to solving conic section problems is identifying which type you're dealing with. Look at the squared terms! If both x2x^2 and y2y^2 have the same sign, it's a circle or ellipse. Different signs indicate a hyperbola. If only one variable is squared, it's a parabola.

The power of analytical geometry lies in transforming visual problems into equations you can solve systematically. Whether you're dealing with circles, ellipses, hyperbolas, or parabolas, the standard forms give you a clear roadmap to find key features like centers, vertices, foci, and directrices.

We thought you’d never ask...

What is the Knowunity AI companion?

Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.

Where can I download the Knowunity app?

You can download the app in the Google Play Store and in the Apple App Store.

Is Knowunity really free of charge?

That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.

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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user