SOLUTION: with the equation: {{{2x^2-10x+2y^2-18y=1}}} how do I make an equation for a circle {{{(x-h)^2 + (y-k)^2 = r^2}}} I need to solve for center of circle and radius of circe. Thanks!

Algebra ->  Algebra  -> Quadratic-relations-and-conic-sections -> SOLUTION: with the equation: {{{2x^2-10x+2y^2-18y=1}}} how do I make an equation for a circle {{{(x-h)^2 + (y-k)^2 = r^2}}} I need to solve for center of circle and radius of circe. Thanks!      Log On

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Question 155891: with the equation: 2x%5E2-10x%2B2y%5E2-18y=1 how do I make an equation for a circle %28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2 I need to solve for center of circle and radius of circe. Thanks!
Answer by Alan3354(21615) About Me  (Show Source):
You can put this solution on YOUR website!
with the equation: 2x%5E2-10x%2B2y%5E2-18y=1 how do I make an equation for a circle %28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2 I need to solve for center of circle and radius of circe. Thanks!
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You have to complete the squares of the x and y terms.
Divide thru by 2.
x%5E2-5x%2By%5E2-9y=1%2F2
Then add amounts to complete the squares:
x%5E2-5x%2B6.25+%2B+y%5E2-9y%2B20.25=1%2F2+%2B+6.25+%2B+20.25
Collect terms
%28x-2.5%29%5E2+%2B+%28y-4.5%29%5E2+=+27
So the center is at (2.5,4.5), and the radius is 3*sqrt(3)