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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?

 Feb 11, 2020
 #1
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Rearrange as

 

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

 

x^2 - 6x  + y^2  + 2y  = 10      complete the square on x and  y

 

x^2 -6x + 9  + y^2 + 2y + 1  = 10 + 9 + 1      factor

 

(x - 3)^2  + (y +1)^2   =  20

 

This is a circle  with a center of  (3, -1)  and a radius of  √20

 

The  side of the square = twice the radius of the circle  =   2√20  = √80

 

So....the area of the square   =  side^2  =  (√80)^2 =   80  units^2

 

 

 

cool cool cool

 Feb 11, 2020

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