Question

The equation of a circle is x2 + y2 - 12y + 20 = 0

What are the coordinates of the center and the length of the radius of the circle?

Answer 1

Center: (0, 6); radius = 4

Explanation:

x^2 + y^2 - 12y + 20 = 0

We must complete the square in y.

x^2 + y^2 - 12y = -20

x^2 + y^2 - 12y + 36 = -20 + 36

x^2 + (y - 6)^2 = 16

(x - 0)^2 + (y - 6)^2 = 4^2

Center: (0, 6); radius = 4