Chapter 9.5, Problem 33PPS

a.

To determine

Make a table for given value.

Answer to Problem 33PPS

  

Explanation of Solution

Given information:

  $xy=16$ .

Value for the equation for $-12\le x\le 12$ .

Calculation:

Consider the equation,

  $xy=\mathrm{16.......}(1)$

Put the corresponding values for $y$ for $-12\le x\le 12$ using $ti-83$ calculator as follows: Press $"Y="$ key. Insert the given equation as a function of $y$ .

  

Press $"2^{nd}"$ key and then “Window” Key. Set $Tb1Start=-12and\Delta TbI=2$ .

  

Press $"2^{nd}"$ Key and then “Graph” key. The table of values is as follows:

  

b.

To determine

Plot a graph of hyperbola.

Answer to Problem 33PPS

  

Explanation of Solution

Given information:

  $xy=16$

Calculation:

The graph of equation $xy=16$ is as follows:

  

c.

To determine

Graph the asymptotes for the hyperbola.

Answer to Problem 33PPS

  

Explanation of Solution

Given information:

  $xy=16$

Calculation:

The graph of given equation $xy=16$ approaches to $Y-axis$ but does not touch it for the values of $x$ form $x=-1tox=1.$ . The graph also approaches to $X-axis$ but does not touch it for the lesser values of $x$ . Hence, “ $X-axis$ and the $Y-axis$ ” will be the asymptotes of the graph.

The graph is shown below:

  

d.

To determine

Determine the special properties of asymptotes.

Answer to Problem 33PPS

Rectangular hyperbola , Proved.

Explanation of Solution

Given information:

  $xy=16$

Calculation:

The asymptotes of the given graph $xy=16$ are “Perpendicular.”

Hence, the hyperbola $xy=16$ is a rectangular hyperbola.

e.

To determine

Find the coordinates of the given vertices.

Answer to Problem 33PPS

  $\left(-5,-5\right)and\left(5,5\right)$ & $\left(-6,-6\right)and\left(6,6\right)$

Explanation of Solution

Given information:

  $xy=16$

The coordinates of the vertices for $xy=25?for,xy=36?$

Calculation:

The vertices of hyperbola $xy=16$ are $\left(-4,-4\right)and\left(4,4\right)$ , the vertices for the hyperbola $xy=25$ will be $\left(-5,-5\right)and\left(5,5\right)$ and the coordinates of vertices for hyperbola $xy=36$ will be $\left(-6,-6\right)and\left(6,6\right).$