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For what value of c will the circle with equation x^2 - 10x + y^2 + 8y + c = 0 have a radius of length \(1\)?

 Feb 9, 2022
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(x^2 -10x)     +    ( y^2 + 8y)    = - c      complete the square for x and y

(x-5)^2          +   ( y  +4)^2      = - c      + 25  + 16     < === the red portion = radius squared

                                                  - c + 41 = 1 ^2

                                                   -c = - 40                          c = 40

 Feb 9, 2022

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