Question

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

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

Answer 1

The equation is (x + 1)^2 + (y + 2)^2 = 15

Center is at (-1, -2) and radius = √15

Explanation:

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

Divide through by 2:-

x^2 + y^2 + 2x + 4y - 10 = 0

x^2 + 2x + y^2 + 4x = 10

Completing the square on the x and y terms:-

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

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

(x + 1)^2 + (y + 2)^2 = 15