Question

In the following exercises, graph.

$16y^2-25x^2=400$

Short answer

The graph is

Step-by-step solution

Step 1. Given information

The equation is $16y^2-25x^2=400$.

Draw the graph.

Step 2. Calculation

Divide the equation by 400 and simplify.

$$\begin{gathered} \frac{16y^2}{400}-\frac{25x^2}{400}=\frac{400}{400} \\ \frac{y^2}{25}-\frac{x^2}{16}=1 \end{gathered}$$

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

Here, $a^2=25\Rightarrow a=\pm 5$

So, the vertices on y- axis are $\left(0,5\right),\left(0,-5\right)$

Now, $b^2=16\Rightarrow b=\pm 4$

The vertices on x- axis are $\left(4,0\right),\left(-4,0\right)$

So asymptote have the equations,

$y=\frac{5}{4}x$

$y=-\frac{5}{4}x$

Step 3. Draw  the graph

Draw the graph using asymptotes.