Question

In Problems 37–40, write an equation for each hyperbola.

Short answer

Equation of hyperbola is:$\frac{y^2}{36}-\frac{x^2}{9}=1$

Step-by-step solution

Step 1. Given information

Graph of the hyperbola:

Step 2. Finding the equation of hyperbola

Comparing information from the graph with standard form of hyperbola,

$$\begin{gathered} \mathrm{Vertices}=(0,\pm 6)=(0,\pm a) \\ \mathrm{Asymptotes}=\pm 2x=\pm \frac{a}{b}x \\ \Rightarrow a=6,b=3 \end{gathered}$$

Equation of hyperbola is:

$$\begin{gathered} \frac{y^2}{6^2}-\frac{x^2}{3^2}=1 \\ \Rightarrow \frac{y^2}{36}-\frac{x^2}{9}=1 \end{gathered}$$