The circle 2x^2 = -2y^2 + 2x - 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?
+129845 Rearrange as
2x^2 -2x + 2y^2 + 4y = 20 divide through by 2
x^2 - x + y^2 + 2y = 10 complete the square on x and y
x^2 - x + 1/4 + y^2 + 2y + 1 = 10 + 1/4 + 1
(x - 1/2)^2 + ( y + 1)^2 = 11.25
The radius = r^2 = 11.25
The area of the square = (2r) ( 2r) = 4r^2 = 4 (11.25) = 45 units ^2
