The circle 2x^2 = -2y^2 + 12x - 4y + 20 + y^2 + x^2 is inscribed inside a square which has a pair of sides parallel to the x-axis. What is the area of the square?
+128474 2x^2 = - 2y^2 + 12x - 4y + 20 + y^2 + x^2
Rearrange as
x^2 - 12x + y^2 - 4y = 20 complete the square on x,y
x^2 -12x + 36 + y^2 - 4y + 4 = 20 + 36 + 4
(x - 6)^2 + (y - 2)^2 = 60
The radius of the circle = sqrt (60)
So the side of the square is twice this = 2sqrt (60)
Area of the square = [ 2sqrt (60) ] ^2 = 4 * 60 = 240
