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Let C be the circle with equation x^2+2y-9=-y^2+28x+19$. If (a,b) is the center of C and r is its radius, what is the value of a+b+r?

 Aug 3, 2021
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x^2+2y-9=-y^2+28x+19      re-arrange into   circle form   (x-h)^2 + (y-k)^2 = r^2

 

x^2 -28x        + y^2 + 2y    = 28    complete the square forx and y

(x-14)^2        + (y+1)^2     = 196 + 28 + 1

 

center = 14, -1        r = sqrt (196+28+1)      I think you can finish !    cheeky

 Aug 3, 2021

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