Find the center and radius of the circle with equation (x + 2)² + (y - 2)² = 36?

Solution:

If P(x, y) is the point which lies on the circle with its centre at (h, k), then the general equation of the circle can be expressed as:

\(\sqrt{(x-h)^{2} + (y-k)^{2}} = r\)(1)

Where r is the radius of the circle.

Squaring the above equation we get

\({(x-h)^{2} + (y-k)^{2}} = r^{2}\)(2)

Comparing equation (2) with the given equation i.e.  (x + 2)² + (y - 2)² = 36 we can infer:

Center of the Circle = (-2, 2) and the radius of the circle is 6 because 

h = -2 and k = 2.

r² = 36 ⇒ r = 6

Find the center and radius of the circle with equation (x + 2)² + (y - 2)² = 36?

Summary:

 The center and radius of the circle with equation (x + 2)² + (y - 2)² = 36 is (-2, 2) and 6 respectively.