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The circle 2x^2 = -2y^2 + 2x - 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?

 Jun 24, 2021
 #1
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Rearrange  as

 

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

 

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

 

x^2  -  x  +  1/4  + y^2  + 2y  + 1 = 10  +  1/4 + 1

 

(x   -  1/2)^2   +  ( y + 1)^2   = 11.25

 

The  radius  =  r^2  =  11.25

 

The  area of the square  =  (2r)  ( 2r)  =  4r^2  =   4 (11.25)   =  45  units ^2

 

cool cool cool

 Jun 24, 2021
edited by CPhill  Jun 24, 2021

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