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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?

 Jan 1, 2022
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( x2 + 6x + ... ) + ( y2 - 14y + ... )  =  -c

 

Completing the square:  ( x2 + 6x + 9 ) + ( y2 - 14y + 49 )  =  -c + 9 + 49

                                                               (x + 3)2 + (y - 7)2  =  58 - c

 

For the radius to equal 4,  58 - c  =  16     --->     -c  =  -42     --->     c  =  42

 Jan 1, 2022

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