Use completing the square to rewrite the equation in the form (x-h)^2 + (y-k)^2 = r^2. State the center (h,k) and radius (r) of the circle.

Question

2x^2 + 2y^2 + 4x + 8y - 20 = 0

Answer 1

Divide by 2 and rearrange terms to get: (x² + 2x) + (y²+4y) = 10

[(1/2)(2)]² = 1 and [(1/2)(4)]² = 4

(x² + 2x +1) + (y² + 4y + 4) = 10 + 1 + 4

(x+1)² + (y+2)² = 15

[x - (-1)]² + [y - (-2)]² = (√15)²

center = (-1,-2) and radius = √15