The circle $2x^2 = -2y^2 + 12x - 4y + 20$ is inscribed inside a square which has a pair of sides parallel to the x-axis. What is the area of the square?
+128474 Rearrange as
2x^2 - 12x + 2y^2 + 4y = 20 divide through by 2
x^2 - 6x + y^2 + 2y = 10 complete the square on x and y
x^2 -6x + 9 + y^2 + 2y + 1 = 10 + 9 + 1 factor
(x - 3)^2 + (y +1)^2 = 20
This is a circle with a center of (3, -1) and a radius of √20
The side of the square = twice the radius of the circle = 2√20 = √80
So....the area of the square = side^2 = (√80)^2 = 80 units^2
