SOLUTION: find all the information for this problem x^2+y^2+6x-6y=2 i thought this problem was an ellipse but couldnt figure it out.

Algebra ->  Algebra  -> Quadratic-relations-and-conic-sections -> SOLUTION: find all the information for this problem x^2+y^2+6x-6y=2 i thought this problem was an ellipse but couldnt figure it out.      Log On

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Question 29289: find all the information for this problem x^2+y^2+6x-6y=2
i thought this problem was an ellipse but couldnt figure it out.
Found 2 solutions by Earlsdon, Nate:
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
You might want to try this:
x%5E2%2By%5E2%2B6x-6y+=+2 Group the x-terms and the y-terms.
%28x%5E2%2B6x%29%2B%28y%5E2-6y%29+=+2 Now "complete the square" in the x-terms and in the y-terms.
%28x%5E2%2B6x%2B9%29%2B%28y%5E2-6y%2B9%29+=+2%2B18 Simplify and factor the parentheses.
%28x%2B3%29%5E2+%2B+%28y-3%29%5E2+=+20 Does this begin to look familiar? Compare with:
%28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2 A circle with centre at (h, k) and radius r.
You should be able to draw the conclusion yourself.

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
Since the coefficients of both x^2 and y^2 are the same and are being added, it is a circle!