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The circle 2x^2 = -2y^2 + 12x - 4y + 28 is inscribed inside a square which has a pair of sides parallel to the x-axis. What is the area of the square?

 Apr 10, 2021
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 2x^2 = -2y^2 + 12x - 4y + 28

 

To  make  things easier,  divide  through  by 2  and rearrange  as 

 

x^2  - 6x  +  y^2 + 2y  =  14         complete  the  square on  x and  y

 

x^2  -  6x  +  9  +  y^2 + 2y  + 1  =   14  + 9  +  1

 

(x - 3)^2   +  (y + 1)^2  =   24

 

The  radius  =  sqrt (24)   and  the diameter     =   the side of the  square  =  2sqrt (24)

 

So.....the   area of the square =  (2sqrt 24)^2   =  4 * 24   =  96  units^2 

 

 

cool cool cool

 Apr 10, 2021

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