Question

In the following exercises, graph

$4y^2-9x^2=36$

Short answer

The graph is

Step-by-step solution

Step 1. Given information

The equation is $4y^2-9x^2=36$.

Draw the graph.

Step 2. Calculation

Divide the equation by 36 and simply

$$\begin{gathered} \frac{4y^2}{36}-\frac{9x^2}{36}=\frac{36}{36} \\ \frac{y^2}{9}-\frac{x^2}{4}=1 \end{gathered}$$

The $y^2$term is positive, the transverse axis is vertical.

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

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

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

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

So asymptote have the equations,

localid="1645809347488" $y=\frac{3}{2}x$

localid="1645809365129" $y=-\frac{3}{2}x$

Step 3. Draw the graph

Draw the graph using asymptotes.