+1242 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?
Re-arrange to find the radius of the circle:
2x^2 - 12x + 2y^2 +4y = 20 divide through by 2
x^2-6x + y^2 + 2y = 10 complete the squares for x and y
(x -3)^2 + (y+1)^2 = 10 +9 +1
radius = sqrt 20
2 x radius =diameter AND diagonal of square
2 sqrt20 = diagonal of square
s^2 + s^2 = (2 sqrt20)^2 (pythagorean theorem)
2 s^2 = 80
s^2 =40
s = sqrt 40 area = sqrt40 x sqrt 40 = 40 sq units
