Question

In the following exercises, graph.

$\frac{x^2}{25}-\frac{y^2}{9}=1$

Short answer

The graph is

Step-by-step solution

Step 1. Given information

The equation is $\frac{x^2}{25}-\frac{y^2}{9}=1$

Draw the graph.

Step 2. Calculation

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

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

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

Now, localid="1645323346112" $b^2=9\Rightarrow b=\pm 3$

The vertices on y- axis are localid="1645323362654" $\left(0,3\right),\left(0,-3\right)$

So asymptote have the equations,

localid="1645323381754" $y=\frac{3}{5}x$

localid="1645323410074" $y=-\frac{3}{5}x$

Step 3. Draw the graph

Draw the graph using asymptote.