Question

In the following exercises, graph.

$\frac{x^2}{16}-\frac{y^2}{25}=1$

Short answer

The graph is

Step-by-step solution

Step 1. Given information

The equation is $\frac{x^2}{16}-\frac{y^2}{25}=1$

Draw the graph.

Step 2. Calculation 

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

So, $a^2=16\Rightarrow a=\pm 4$

So, the vertices on x- axis are $\left(4,0\right),\left(-4,0\right)$.

Now, $b^2=25\Rightarrow b=\pm 5$

The vertices on y- axis are $\left(0,5\right),\left(0,-5\right)$.

So asymptote have the equations,

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

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

Step 3. Draw the graph.

Draw the graph using asymptote.