So the equation (below) is an ellipse, but how would I tell its an ellipse/hyperbola/parabola just from looking at the equation?
Hi gomes,
If you are given an equation of the form:
$\displaystyle Ax^2+Bxy+Cy^2+Dx+Ey+F=0$ with $\displaystyle B =0$,
you can determine the type of conic section just by considering the values of A and C.
If A = 0 or C = 0, but not both, then the conic is a parabola.
If A = C, then the conic is a circle.
If A and C have the same sign, but $\displaystyle A \neq C$, then the conic is an ellipse.
If A and C have opposite signs, then the conic is a hyperbola.
Read this: Ellipses and Hyperbolae
(Which I'm sure will also be in your classnotes and/or textbook).