# How can I tell the equation of a hyperbola from the equation of an ellipse?

Oct 7, 2014

When both ${X}^{2}$ and ${Y}^{2}$ are on the same side of the equation and they have the same signs, then the equation is that of an ellipse. If the signs are different, the equation is that of a hyperbola

Example:

${X}^{2} / 4 + {Y}^{2} / 9 = 1$
$9 {X}^{2} + 4 {Y}^{2} = 36$

For both cases, X and Y are positive. Hence Ellipse.

${X}^{2} / 4 - {Y}^{2} / 9 = 1$
$9 {Y}^{2} - 4 {X}^{2} = 36$

For these cases, X and Y have different signs. Hence hyperbola