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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?

 Jul 7, 2022
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2x^2  = -2y^2 + 12x - 4y  + 28     rearrange  as

 

2x^2 - 12x + 2y^2 + 4y   =  28          divide through by 2

 

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

 

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

 

( x - 3)^2  +  ( y + 1)^2  =   24

 

The radius of the square =   sqrt (24)

 

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

 Jul 7, 2022

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