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

Printable View

- Jun 7th 2010, 12:53 PMgomesellipse
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, 01:02 PMmasters
Hi gomes,

If you are given an equation of the form:

with ,

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 , then the conic is an ellipse.

If A and C have opposite signs, then the conic is a hyperbola. - Jun 7th 2010, 05:08 PMmr fantastic
Read this: Ellipses and Hyperbolae

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