Question

Graphs of Hyperbolas Match the equation with the graphs labeled I-IV. Give reasons for your answers.

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

Short answer

The graph of the hyperbola$\frac{x^2}{4}-y^2=1$matched it with the graph labeled as3 .

Step-by-step solution

Step 1. Given information.

The hyperbola equation $\frac{x^2}{4}-y^2=1$

Step 2. The graph of the hyperbola and match it with given graphs labeled asI-IV .

We will convert the given equation of the hyperbola in the standard form and then by comparing we will get the values of a, b.

Writing the given hyperbola equation in standard form we get,

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

On comparing the giving hyperbola equation with the standard hyperbola equation we get,

$\begin{array}{l}a=2\\ b=1\end{array}$

Hence the vertices are$(\pm 2,0)$

And the transverse axis is horizontal.
Therefore the graph labeled as 3 is the correct answer.