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avatar+794 

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?

 

The reason i keep reposting is that i keep getting troll answers. I have no clue how they got the radius in that answer.

 Jun 1, 2020
 #1
avatar+21955 
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                   2x2 =  -2y2 + 12x - 4y + 20

Divide by 2:  x2 =  -y2 + 6x - 2y + 10

Rearrange:                           x2 - 6x      + y2 + 2y        =  10

Complete the square on x:  x2 - 6x + 9 + y2 + 2y        =  10 + 9

Complete the square on y:  x2 - 6x + 9 + y2 + 2y + 1  =  10 + 9 + 1

Simplify:                                           (x - 3)2 + (y + 1)2 =  20

 

This means the the center is at (3, -1) and the radius:  r  =  sqrt(20)

 

So the width of the square is twice the radius:  width  =  2·sqrt(20)

 

And th area is:  [ 2·sqrt(20) ]2  =  4·20  =  80  

 Jun 2, 2020
 #2
avatar+794 
0

Thank you!!!

AnimalMaster  Jun 2, 2020

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