Question

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

Short answer

Equation of hyperbola is:$\frac{x^2}{4}-\frac{y^2}{16}=1$

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,

$$\begin{gathered} \mathrm{Vertices}=(\pm 2,0)=(\pm a,0) \\ \mathrm{Asymptotes}=\pm 2x=\pm \frac{b}{a}x \\ \Rightarrow a=2,b=4 \end{gathered}$$

Equation of hyperbola is:

$$\begin{gathered} \frac{x^2}{2^2}-\frac{y^2}{4^2}=1 \\ \Rightarrow \frac{x^2}{4}-\frac{y^2}{16}=1 \end{gathered}$$