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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?

 May 2, 2019
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Re-arrange to find the radius of the circle:

2x^2 - 12x + 2y^2 +4y = 20     divide through by 2

  x^2-6x + y^2 + 2y = 10      complete the squares for x and y

(x -3)^2   + (y+1)^2  = 10 +9 +1

    radius = sqrt 20

2 x radius =diameter AND diagonal of square

2 sqrt20 = diagonal of square

s^2 + s^2 = (2 sqrt20)^2   (pythagorean theorem)

2 s^2 = 80

s^2 =40

s = sqrt 40        area = sqrt40 x sqrt 40 = 40 sq units     

 May 2, 2019

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