Question

Find the center and radius of
x2 + y2 + 2x – 10y + 10 = 0

Answer 1

x^2 + y^2 + 2x – 10y + 10 = 0

x^2 + 2x + y^2 - 10y = 0

We must complete the square in x and y.

(x^2 + 2x + 1) + (y^2 -10y + 25) = 4 + 25

(x + 1)^2 + (y - 5)^2 = 29

The radius r is found solving r^2 = 29 for y.

(x + 1)^2 + (y - 5)^2 = sqrt{29}

See picture for the center and radius.