Find the coordinates of the centre radius of each of the following circle:

Question

Philoid · Accepted Answer

Given: the equation of the circle is

⇒ x² + y² + 2xcosθ + 2ysinθ - 8 = 0 ..... (1)

We know that for a circle

x² + y² + 2ax + 2by + c = 0 .... (2)

⇒ Centre = (- a, - b)

⇒ Radius =

Comparing (1) with (2) we get,

⇒ Centre =

⇒ Centre = (- cosθ, - sinθ)

⇒ Radius =

⇒ Radius = √9

⇒ Radius = 3

∴ The centre and radius of the circle is (- cosθ, - sinθ) and 3.