---
title: Circle Equations
---
## Circle Equations
![Circle centered at (x0, y0) with radius r, a point P(x, y) on the circle, and angle t](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_2.gif)
### 1. Centre-radius form:
Circle having centre (x0, y0) and radius r.
The equation of the circle can be represented as:
![(x-x0)^2 + (y-y0)^2 = r^2](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_3.png)
#### General Equation of a Circle:
![x^2 + y^2 + 2gx + 2fy + c = 0](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_6.png)
where, `g`, `f`, and `c` are constants.
Therefore,
![x0 = (-g), y0 = (-f), and r = square root of (g^2 + f^2 -c)](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_9.png)
### 2. Parametric form:
Circle having centre (x0, y0) and radius makes an angle t with the positive direction of x-axis, then t is called the `parameter`.
The equation of the circle can be represented as:
![x = x0 + rcos(t), y = y0 + rsin(t)](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_4.png)
for,
![0<=t<= 2 pi](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_5.png)
### More Information:
Equation of a Circle