Thread: ellipse

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

Originally Posted by gomes

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:

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.

Originally Posted by gomes

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

Read this: Ellipses and Hyperbolae

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