# How do I determine whether a hyperbola opens horizontally or vertically?

Oct 12, 2014

Make the equation be in the form

${\left(x - h\right)}^{2} / {a}^{2} - {\left(y - k\right)}^{2} / {b}^{2} = 1$

or

${\left(y - k\right)}^{2} / {a}^{2} - {\left(x - h\right)}^{2} / {b}^{2} = 1$

If $x$ is on front, the hyperbola opens horizontally
If $y$ is on front, the hyperbola opens vertically