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The equation of a circle which has a center at (-5, 2) can be written as Ax^2 + 2y^2 + Bx + Cy = 40. Find the radius of the circle

 Feb 27, 2021
 #1
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I believe   A will ahve to equal the  y^2 coefficient ....or you will wind up with an ellipse rather than a circle....

 

2x^2 + Bx     + 2y^2 + C y   = 40

 

 

divide thru by 2  

x^2 + bx         + y^2 + cy       = 20

 

Center is given as  (-5,2)

(x+ b/2)2      +  (y + c/2)^2     = 20  +.....                  - b/2 = -5   

                                                                                - c/2 =  

 

 

so you have 

(x+5)^2        +     ( y - 2)^2    =   20 +  25  + 4

                                             = 49                                   49 is r^2                 so      r = 7

 

x^2 + 25x + 25     + y^2 - 4y + 4 = 49

x^2 + 25x              + y^2 -4y       = 49 - 25 -4 = 20

2x2  + 2y2  + 50x    + (- 8) y   = 40       Check!

 Feb 27, 2021

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