Circles

Definition of a circle

A circle is defined as the locus of a point that moves in a plane such that its distance from the fixed point in that plane is always constant.

For a circle, as given earlier, e = 0. The directrix is at infinity.

∴ CP = a

where P is the locus given by (x,y), “a” is the radius of the circle and C is the center and the focus of the circle.

Example 1

Find the equation of a circle whose center is (-2 -3) and radius is 4.

Example 2

Find the center and radius of the circle whose equation is :

Try these questions

  1. Find the equation of a circle whose radius is 3 and origin is at the center.

  2. Find the center and radius of the circle whose equation is: