Question

In the following exercises, graph.

$\frac{x^2}{9}-\frac{y^2}{36}=1$

Short answer

The graph is

Step-by-step solution

Step 1. Given information

The equation is $\frac{x^2}{9}-\frac{y^2}{36}=1$

Draw the graph.

Step 2. Calculation

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

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

So, the vertices on x- axis are $\left(3,0\right),\left(-3,0\right)$

Now, $b^2=36\Rightarrow b=\pm 6$

The vertices on y- axis are $\left(0,6\right),\left(0,-6\right)$.

So asymptote have the equations,

$$\begin{gathered} y=\frac{6}{3}x \\ =2x \end{gathered}$$

$$\begin{gathered} y=-\frac{6}{3}x \\ =-2x \end{gathered}$$

Step 3. Draw the graph 

Draw the graph using asymptote.