Question

Find the center of a circle with the equation: x^2 + y^2 - 2y - 8x - 19 = 0

Answer 1

(4, 1)

Explanation:

x^2 + y^2 - 2y - 8x - 19 = 0

We rearrange the terms and complete the square twice.

x^2 - 8x + y^2 - 2y = 19

x^2 - 8x + 16 + y^2 - 2y + 1 = 19 + 16 + 1

(x - 4)^2 + (y - 1)^2 = 6^2

The center is (4, 1)