# Circle in a Cartesian Plane

## Circle in a Cartesian Plane

The locus of all the points with coordinates (x, y) that are equidistant from a fixed point called the centre of the circle.

The distance between the points on the circle and its centre is called the radius of the circle.
If the coordinates of the centre are (0, 0), the circle is said to be centred at the origin.

The equation of a circle with radius r and centred at the origin of a Cartesian coordinate system is :$$x^2 + y^2=r^2$$.

The equation of a circle with radius r and centred at a point with coordinates C(hk) in a Cartesian coordinate system is : $$(x-h)^2 + (y-k)^2=r^2$$.

### Example

Consider a circle whose centre is C(6, 2), whose radius is 5 and whose equation is : $$(x-6)^2 + (y-2)^2=25$$

Therefore h = 6 and k = 2