41 lines
1.4 KiB
Markdown
41 lines
1.4 KiB
Markdown
|
---
|
|||
|
title: Circle Equations
|
|||
|
localeTitle: 圆方程
|
|||
|
---
|
|||
|
## 圆方程
|
|||
|
|
|||
|
![圆以(x0,y0)为中心,半径为r,圆上的点为P(x,y),角度为t](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_2.gif)
|
|||
|
|
|||
|
### 1.中心半径形式:
|
|||
|
|
|||
|
具有中心_**(x 0 ,y 0 )**_和半径**_r的_**圆。
|
|||
|
|
|||
|
圆的方程可以表示为:
|
|||
|
|
|||
|
![(x-x0)^ 2 +(y-y0)^ 2 = r ^ 2](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_3.png)
|
|||
|
|
|||
|
#### 圆的一般方程:
|
|||
|
|
|||
|
![x ^ 2 + y ^ 2 + 2gx + 2fy + c = 0](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_6.png)
|
|||
|
|
|||
|
其中, `g` , `f`和`c`是常数。
|
|||
|
|
|||
|
因此,
|
|||
|
|
|||
|
![x0 =( - g),y0 =( - f),r =(g ^ 2 + f ^ 2 -c)的平方根](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_9.png)
|
|||
|
|
|||
|
### 2.参数形式:
|
|||
|
|
|||
|
具有中心_**(x 0 ,y 0 )**_和半径的圆与_x轴_的正方向形成角度**_t_** ,然后**_t_**被称为`parameter` 。
|
|||
|
|
|||
|
圆的方程可以表示为:
|
|||
|
|
|||
|
![x = x0 + rcos(t),y = y0 + rsin(t)](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_4.png)
|
|||
|
|
|||
|
对于,
|
|||
|
|
|||
|
![0 <= t <= 2 pi](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_5.png)
|
|||
|
|
|||
|
### 更多信息:
|
|||
|
|
|||
|
[圆的方程](http://mypages.valdosta.edu/alazari/math1111/Circle.html)
|