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For what value of k does the equation x^2+10x+y^2+16y-k=0 represent a circle of radius 6?

 Jan 14, 2022
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x^2+10x+y^2+16y   = k        now complete the square for x and y

(x+5)^2     +  ( y+8)^2   = 25 + 64  +k      the red part = r^2    ( which = 6^2 = 36) 

 

r^2 = 89 + k    = 36    solve for k

         k = -53

 Jan 14, 2022

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