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?
The reason i keep reposting is that i keep getting troll answers. I have no clue how they got the radius in that answer.
2x2 = -2y2 + 12x - 4y + 20
Divide by 2: x2 = -y2 + 6x - 2y + 10
Rearrange: x2 - 6x + y2 + 2y = 10
Complete the square on x: x2 - 6x + 9 + y2 + 2y = 10 + 9
Complete the square on y: x2 - 6x + 9 + y2 + 2y + 1 = 10 + 9 + 1
Simplify: (x - 3)2 + (y + 1)2 = 20
This means the the center is at (3, -1) and the radius: r = sqrt(20)
So the width of the square is twice the radius: width = 2·sqrt(20)
And th area is: [ 2·sqrt(20) ]2 = 4·20 = 80