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?
+128473 2x^2 = -2y^2 + 12x - 4y + 28 rearrange as
2x^2 - 12x + 2y^2 + 4y = 28 divide through by 2
x^2 - 6x + y^2 + 2y = 14 complete the square on x, y
x^2 -6x + 9 + y^2 + 2y + 1 = 14 + 9 + 1
( x - 3)^2 + ( y + 1)^2 = 24
The radius of the square = sqrt (24)
The diameter= the side of the square = 2sqrt (24)
So.....the area of the square = ( 2sqrt (24))^2 = 4 * 24 = 96 units^2
