# ellipse

• Jun 7th 2010, 11:53 AM
gomes
ellipse
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 PM
masters
Quote:

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

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 PM
mr fantastic
Quote:

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

Read this: Ellipses and Hyperbolae

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