SOLUTION: I need to find the center and radius by hand and having difficulty; x^2-10x+y^2+6y=15

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: I need to find the center and radius by hand and having difficulty; x^2-10x+y^2+6y=15      Log On


   

Question 1077350: I need to find the center and radius by hand and having difficulty;
x^2-10x+y^2+6y=15
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E2-10x%2By%5E2%2B6y=15+ can be rewritten by completing the squares:
+%28x%5E2-10x+%2B+25%29+%2B+%28y%5E2%2B6y+%2B+9%29+=+15+%2B+9+%2B+25+
++%28x-5%29%5E2+%2B+%28y%2B3%29%5E2+=+49+
Compare this to the general form of the equation of a circle +%28x-x%5B0%5D%29%5E2+%2B+%28y-y%5B0%5D%29%5E2+=+r%5E2+
where (+x%5B0%5D+, y%5B0%5D) = coordinates of the center
and you get

center at ( +highlight%285%29+ ,+highlight%28-3%29+ ) and r+=+sqrt%2849%29+=+highlight%287%29%29