What is Circle ???

A circle is a simple closed shape. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant.

More information about circle

Numerical: Find the equation of the circle with centre (–3, 2) and radius 4.

Solution Here h = –3, k = 2 and r = 4. Therefore, the equation of the required circle is

(x + 3)2 + (y –2)2 = 16

Numerical: Find the centre and the radius of the circle x2 + y2 + 8x + 10y – 8 = 0

Solution The given equation is (x2 + 8x) + (y2 + 10y) = 8

Completing the squares, we get

(x2 + 8x + 16) + (y2 + 10y + 25) = 8 + 16 + 25

i.e. (x + 4)2 + (y + 5)2 = 49 = 72

Therefore, the given circle has centre at (– 4, –5) and radius 7.