# What type of conic section has the equation 9x^2-4y^2=36?

Sep 25, 2014

This equation is almost in the form that we need to easily graph and identify.

$9 {x}^{2} - 4 {y}^{2} = 36$

Divide all terms by 36.

$\frac{9 {x}^{2}}{36} - \frac{4 {y}^{2}}{36} = \frac{36}{36}$

Simplify

$\frac{{x}^{2}}{4} - \frac{{y}^{2}}{9} = 1$

Be more explicit with the numerator of each term.

$\frac{{\left(x - 0\right)}^{2}}{4} - \frac{{\left(y - 0\right)}^{2}}{9} = 1 \implies H y p e r b o l a$