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For what value of c will the circle with equation x^2 + 6x + y^2 - 14y + c = 0 have a radius of length 4?

 Jul 7, 2022
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x^2 + 6x + y^2 - 14y = -c         complete the square on x,y

 

x^2 + 6x + 9 + y^2 - 14y + 49  = -c + 9 + 49

 

To have a radius of 4

 

-c + 9 + 49   must  = 16

 

So

 

-c  =  16 - 9 - 49

 

-c = -24

 

c =  24

 

cool cool cool

 Jul 7, 2022

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