Chapter 11.3, Problem 30E

To determine

To graph the hyperbola using graphing device.

Explanation of Solution

Given information: Use graphing device to graph the hyperbola $\frac{x^2}{100}-\frac{y^2}{64}=1$ .

Graph: to draw the graph using a graphing device, it is needed to solve equation for y.

  $\begin{array}{l}\frac{x^2}{100}-\frac{y^2}{64}=1\\ -\frac{y^2}{64}=1-\frac{x^2}{100}\text{ [subtract }\frac{x^2}{100}]\\ -\frac{y^2}{64}=\frac{100-x^2}{100}\text{ [simplify]}\\ y^2=64\left(\frac{x^2-100}{100}\right)\text{ [multiply by 64]}\\ y^2=\pm \frac{64}{100}\sqrt{x^2-100}\text{ [factor 64 and 100]}\\ y=\pm \frac{4}{5}\sqrt{x^2-100}\text{ [sqaure root and simplify]}\end{array}$

To obtain the graph of the hyperbola, graph the following functions,

  $y=\frac{4}{5}\sqrt{x^2-100}\text{ ,}y=-\frac{4}{5}\sqrt{x^2-100}$

Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press $\boxed{\text{Y=}}$ button.

Step 3: Enter the expression $y=\frac{4}{5}\sqrt{x^2-100}\text{ , and }y=-\frac{4}{5}\sqrt{x^2-100}$ which is required to graph.

Step 4: Press GRAPH button to graph the function.

The graph is obtained as:

  

Interpretation:

From the above graph, it can be observed that the vertices of the hyperbola is $\left(\pm 10,0\right)$ and foci is $\left(\pm 2\sqrt{41},0\right)$ and asymptote is $y=\pm \frac{4}{5}x$ .