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算数算数80 views·Updated Jun 3, 2026·1 page

直線と円の方程式：基本から応用まで

座標平面での直線と円の方程式は、数学IIの中でもめちゃくちゃ重要な分野だよ。テストでもよく出るし、実際にグラフを描いて視覚的に理解できるから、意外と楽しく学べるはずだ。

1
of 1
# 直線と円の方程式 (Equations of Lines and Circles) 1. 概要 2. 重要な定義と概念 * **直線の傾き** * 直線 $ax + by + c = 0$ の傾きは $-\frac{a}{b}$ (ただし、$b \neq

直線と円の方程式の基本

君たちが普段見ているスマホの画面も、実は座標で表現されているんだ。直線の方程式には3つの形があって、それぞれ使い分けが重要だよ。

標準形 y=mx+cy = mx + c は一番馴染みやすい形だね。mmが傾きで、ccがyy軸との交点を表している。グラフを描くときはこれが一番分かりやすい。

点傾斜形 y−y1=m(x−x1)y - y_1 = m(x - x_1) は、ある点(x1,y1)(x_1, y_1)を通る直線を求めるときに超便利だ。問題でよく「点Aを通り、傾きが2の直線を求めよ」って出てくるでしょ？

一般形 ax+by+c=0ax + by + c = 0 は計算では面倒だけど、2つの直線が平行か垂直かを判断するときに使う。平行なら傾きが同じ、垂直なら傾きの積が−1-1になるよ。

覚えておこう！ 垂直な直線（縦の線）は傾きがないから、x=ax = aの形で表されるんだ。

円の方程式も2つの形がある。標準形 (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2 は中心(h,k)(h, k)、半径rrがすぐ分かるから便利だ。

距離の公式も忘れちゃダメ。2点間の距離は (x2−x1)2+(y2−y1)2\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} で、点と直線の距離は ∣ax0+by0+c∣a2+b2\frac{|ax_0 + by_0 + c|}{\sqrt{a^2 + b^2}} だよ。これらは暗記必須だから、何度も練習して体に染み込ませよう！

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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.

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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 SiOS 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 KlichAndroid 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.

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算数算数80 views·Updated Jun 3, 2026·1 page

直線と円の方程式：基本から応用まで

座標平面での直線と円の方程式は、数学IIの中でもめちゃくちゃ重要な分野だよ。テストでもよく出るし、実際にグラフを描いて視覚的に理解できるから、意外と楽しく学べるはずだ。

1
of 1
# 直線と円の方程式 (Equations of Lines and Circles) 1. 概要 2. 重要な定義と概念 * **直線の傾き** * 直線 $ax + by + c = 0$ の傾きは $-\frac{a}{b}$ (ただし、$b \neq

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直線と円の方程式の基本

君たちが普段見ているスマホの画面も、実は座標で表現されているんだ。直線の方程式には3つの形があって、それぞれ使い分けが重要だよ。

標準形 y=mx+cy = mx + c は一番馴染みやすい形だね。mmが傾きで、ccがyy軸との交点を表している。グラフを描くときはこれが一番分かりやすい。

点傾斜形 y−y1=m(x−x1)y - y_1 = m(x - x_1) は、ある点(x1,y1)(x_1, y_1)を通る直線を求めるときに超便利だ。問題でよく「点Aを通り、傾きが2の直線を求めよ」って出てくるでしょ？

一般形 ax+by+c=0ax + by + c = 0 は計算では面倒だけど、2つの直線が平行か垂直かを判断するときに使う。平行なら傾きが同じ、垂直なら傾きの積が−1-1になるよ。

覚えておこう！ 垂直な直線（縦の線）は傾きがないから、x=ax = aの形で表されるんだ。

円の方程式も2つの形がある。標準形 (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2 は中心(h,k)(h, k)、半径rrがすぐ分かるから便利だ。

距離の公式も忘れちゃダメ。2点間の距離は (x2−x1)2+(y2−y1)2\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} で、点と直線の距離は ∣ax0+by0+c∣a2+b2\frac{|ax_0 + by_0 + c|}{\sqrt{a^2 + b^2}} だよ。これらは暗記必須だから、何度も練習して体に染み込ませよう！

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.

Most popular content in 算数

6

Most popular content

9

Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.6/5App Store
4.7/5Google Play

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 SiOS 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 KlichAndroid 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.

AnnaiOS user