# Circles

A circle is the locus of a point which moves in a plane such that its distance from a fixed point is a constant.
The fixed point is called the centre and the constant distance is called the radius of the circle.

The reason why many clock surfaces are circular is that the locus of end of clock's minute hand is a circle.

# Equation of a Circle

Let C(h, k) be the centre and r be the radius of a circle. Let P(x, y) be any point on the circle. Then CP is radius of the circle.
âˆ´ |CP| = r

The equation of circle with centre at the origin and radius r is
.

Example 1:
Find the equation of the circle with centre (2, -3) and passing through (5, -7).
 Solution: Let C be (2, -3) and P be (5, -7). Radius r = CP = . Thus the equation of the circle is i.e., is the required equation.
Example 2:
Find the centre and radius of the circle .
 Solution: i.e., Now completing the squares with in the parenthesis, we get i.e., Here h = 2, k = -4 and r = 5 âˆ´ The centre is the point (2, -4) and radius is 5.