SOLUTION: is 8(2xy+x-x^2)=4(2y^2-y)-100 a parabola, circle, ellipse, or hyperbola

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: is 8(2xy+x-x^2)=4(2y^2-y)-100 a parabola, circle, ellipse, or hyperbola       Log On


   

Question 1066181: is 8(2xy+x-x^2)=4(2y^2-y)-100 a parabola, circle, ellipse, or hyperbola
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
The leading (highest degree terms) are

8x^2 - 16xy + 8y^2 + . . . = 8(x-y)^2 + . . .

After orthogonal transformation u = %28x%2By%29%2Fsqrt%282%29, v = %28x-y%29%2Fsqrt%282%29 you will get this curve in the form

v^2 + {lover degree terms} = 0,

which is a parabola.