SOLUTION: can you please help me how to solve X^2+3y^2-16x+24y+31=0 in standard form. and please state if the equation is a parabola, hyperbola, circle, or ellipse thankyou very much.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: can you please help me how to solve X^2+3y^2-16x+24y+31=0 in standard form. and please state if the equation is a parabola, hyperbola, circle, or ellipse thankyou very much.      Log On


   

Question 309003: can you please help me how to solve X^2+3y^2-16x+24y+31=0 in standard form. and please state if the equation is a parabola, hyperbola, circle, or ellipse thankyou very much.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Complete the square in x and y.
x%5E2%2B3y%5E2-16x%2B24y%2B31=0
x%5E2-16x%2B3y%5E2%2B24y%2B31=0
%28x%5E2-16x%2B64%29%2B3%28y%5E2%2B8y%2B16%29%2B31=64%2B48
%28x-8%29%5E2%2B3%28y%2B4%29%5E2%2B31=112
%28x-8%29%5E2%2B3%28y%2B4%29%5E2=81
%28x-8%29%5E2%2F81%2B%28y%2B4%29%5E2%2F27=1
Unequal coefficients, equal signs points to an ellipse.