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# Analytic Geometry

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Find the radius of the circle with equation x^2 - 4x + y^2 - 6y - 36 = 8x - 20y.

Apr 24, 2022

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Simplify the equation to: \(x^2-12x+y^2+14y=36\)

Complete the square for the left hand side:\((x-6)^2+(y-7)^2\)

Simplifying this gives us: \(x^2-12+y^2+14y+85\)

Since we added 85 to the left hand side, we have to add 85 to the right hand side as well.

This gives us: \((x-6)^2+(y+7)^2=121\)

The right-hand side is the radius squared, so we have the equation: \(121 = r^2\)

Solving, we find \(\color{brown}\boxed{r = 11} \)

Apr 24, 2022