So the equation (below) is an ellipse, but how would I tell its an ellipse/hyperbola/parabola just from looking at the equation?

http://img717.imageshack.us/img717/9693/59640630.jpg

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- Jun 7th 2010, 11:53 AMgomesellipse
So the equation (below) is an ellipse, but how would I tell its an ellipse/hyperbola/parabola just from looking at the equation?

http://img717.imageshack.us/img717/9693/59640630.jpg - Jun 7th 2010, 12:02 PMmasters
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. - Jun 7th 2010, 04:08 PMmr fantastic
Read this: Ellipses and Hyperbolae

(Which I'm sure will also be in your classnotes and/or textbook).