Question

In the following exercises, graph.

$\frac{x^2}{9}-\frac{y^2}{4}=1$

Short answer

The graph is

Step-by-step solution

Step 1. Given information

The equation $\frac{x^2}{9}-\frac{y^2}{4}=1$

Draw the graph.

Step 2. Calculation

The $x^2-$term is positive, the transverse axis is horizontal.

Now, $a^2=9\Rightarrow a=\pm 3$

The vertices on x- axis are $\left(3,0\right),\left(-3,0\right)$.

$b^2=4\Rightarrow b\pm 2$

The vertices on y- axis are $\left(0,2\right),\left(0,-2\right)$.

So asymptote have the equations

$y=\frac{2}{3}x$

$y=-\frac{2}{3}x$

Step 3. Draw the graph

The graph is