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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?

 Jun 28, 2022
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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

 

cool cool cool

 Jun 28, 2022

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