SOLUTION: Find the center and radius of the circle with the given equation. 2x2 + 2y2 − 4x + 12y − 15 = 0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the center and radius of the circle with the given equation. 2x2 + 2y2 − 4x + 12y − 15 = 0       Log On


   

Question 835385: Find the center and radius of the circle with the given equation.
2x2 + 2y2 − 4x + 12y − 15 = 0
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2+%2B+2y%5E2+-+4x+%2B+12y+-+15+=+0
2x%5E2+%2B+2y%5E2+-+4x+%2B+12y=15
2%28x%5E2+%2B+y%5E2+-+2x+%2B+6y%29=15
x%5E2+%2B+y%5E2+-+2x+%2B+6y=15%2F2
x%5E2-2x+%2B+y%5E2%2B6y=15%2F2
x%5E2-2x%2B1+%2B+y%5E2%2B6y%2B9=15%2F2%2B1%2B9
%28x-1%29%5E2+%2B+%28y%2B3%29%5E2=15%2F2%2B10
%28x-1%29%5E2+%2B+%28y%2B3%29%5E2=15%2F2%2B20%2F2
%28x-1%29%5E2+%2B+%28y%2B3%29%5E2=35%2F2
The solution is all the points (x,y) whose distance to point (1,-3) is
sqrt%2835%2F2%29=sqrt%2870%2F4%29=sqrt%2870%29%2Fsqrt%284%29=sqrt%2870%29%2F2
That is the equation of a circle centered at (1,-3), with radius sqrt%2870%29%2F2