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

Oct 20, 2016

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

#### Explanation:

The standard form is ${x}^{2} / {a}^{2} - {y}^{2} / {b}^{2} = 1$
so we must reduce the above equation to this form
Dividing by 9, we get
${x}^{2} / \left(9 \cdot 9\right) - {y}^{2} / \left(\frac{81}{4}\right) = 1$
Rewriting the equation
${x}^{2} / {9}^{2} - {y}^{2} / {\left(\frac{9}{2}\right)}^{2} = 1$
Where $a = 9$ and $b = \frac{9}{2}$