Question

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

Short answer

Equation of hyperbola is:$x^2-y^2=1$

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,

$$\begin{gathered} \mathrm{Vertices}=(\pm 1,0)=(\pm a,0) \\ \mathrm{Asymptotes}=\pm x=\pm \frac{b}{a}x \\ \Rightarrow a=1,b=1 \end{gathered}$$

Equation of hyperbola is:

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