# ellipse

• June 7th 2010, 12:53 PM
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
• June 7th 2010, 01:02 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:

$Ax^2+Bxy+Cy^2+Dx+Ey+F=0$ with $B =0$,

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 $A \neq C$, then the conic is an ellipse.

If A and C have opposite signs, then the conic is a hyperbola.
• June 7th 2010, 05:08 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