SOLUTION: what are the coordinates? Please explain 3x^2+2y^2-12x-4y-136=0 Parabolic? circular? elliptic? hyperbolic?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: what are the coordinates? Please explain 3x^2+2y^2-12x-4y-136=0 Parabolic? circular? elliptic? hyperbolic?      Log On


   

Question 306769: what are the coordinates? Please explain 3x^2+2y^2-12x-4y-136=0
Parabolic? circular? elliptic? hyperbolic?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Coordinates of what exactly?
You can figure out which conic section it is by completing the square in x and y.
3x%5E2%2B2y%5E2-12x-4y-136=0
3x%5E2-12x%2B2y%5E2-4y-136=0
3%28x%5E2-4x%29%2B2%28y%5E2-2y%29-136=0
3%28x%5E2-4x%2B4%29%2B2%28y%5E2-2y%2B1%29-136-12-2=0
3%28x-2%29%5E2%2B2%28y-1%29%5E2-150=0
%28x-2%29%5E2%2F2%2B%28y-1%29%5E2%2F3=150%2F6
%28x-2%29%5E2%2F2%2B%28y-1%29%5E2%2F3=25
%28x-2%29%5E2%2F50%2B%28y-1%29%5E2%2F75=1
It's an ellipse centered at (2,1).