The circle 2x^2 = -2y^2 + 12x - 4y + 28 is inscribed inside a square which has a pair of sides parallel to the x-axis. What is the area of the square?
+128408 2x^2 = -2y^2 + 12x - 4y + 28
To make things easier, divide through by 2 and rearrange as
x^2 - 6x + y^2 + 2y = 14 complete the square on x and y
x^2 - 6x + 9 + y^2 + 2y + 1 = 14 + 9 + 1
(x - 3)^2 + (y + 1)^2 = 24
The radius = sqrt (24) and the diameter = the side of the square = 2sqrt (24)
So.....the area of the square = (2sqrt 24)^2 = 4 * 24 = 96 units^2
