# How do you write the hyperbola 36y^2-4x^2=9 in standard form?

Dec 1, 2016

${y}^{2} / \left(\frac{1}{4}\right) - {x}^{2} / \left(\frac{9}{4}\right) = 1$

#### Explanation:

Write $36 {y}^{2} - 4 {x}^{2} = 9$ in standard form.

Standard form of a hyperbola with a positive ${y}^{2}$ term and a negative ${x}^{2}$ term is $\frac{{\left(y - k\right)}^{2}}{{a}^{2}} - \frac{{\left(x - h\right)}^{2}}{{b}^{2}} = 1$ where $\left(h , k\right)$ is the center.

Divide the equation by 9 to obtain a 1 on the right side.

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

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

Divide each term on the left side by the reciprocal of the coefficient.

${y}^{2} / \left(\frac{1}{4}\right) - {x}^{2} / \left(\frac{9}{4}\right) = 1$

In this example, $\left(h , k\right) = \left(0 , 0\right)$