hyperbola

A two-branch curve where the difference of distances to two fixed points stays constant.

A hyperbola is the set of points $(x,y)$ for which the difference of the distances to two fixed points (the foci) is a constant. Its standard form is $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ (or with $x$ and $y$ swapped), and it graphs as two separate, mirror-image branches that approach a pair of asymptotes but never touch them.

Examples

$\frac{x^2}{9}-\frac{y^2}{4}=1$ is a hyperbola opening left and right along the x-axis.