Chapter 9.3, Problem 57PPS

(a)

To determine

To Graph: Graph formed by union of these two graphs.

Answer to Problem 57PPS

  

Explanation of Solution

Given: $y=\sqrt{9-x^2},y=-\sqrt{9-x^2}$

The graph of union of $y=\sqrt{9-x^2},y=-\sqrt{9-x^2}$ is shown below

  

(b)

To determine

To Write: The equation for the union of two graphs.

Answer to Problem 57PPS

  $x^2+y^2=9$

Explanation of Solution

Given: $y=\sqrt{9-x^2},y=-\sqrt{9-x^2}$

  $y=\sqrt{9-x^2},y=-\sqrt{9-x^2}$

Squaring both the equations we get

  $\begin{array}{l}{y}^2={\left(\sqrt{9-x^2}\right)}^2=9-x^2\\ y^2={\left(-\sqrt{9-x^2}\right)}^2=9-x^2\\ i.e\\ y^2=9-x^2\\ x^2+y^2=9\end{array}$

Hence,

  $x^2+y^2=9$

(c)

To determine

To Describe: The way to graph the equation on the graphing calculator.

Answer to Problem 57PPS

  

Explanation of Solution

Given: $x^2+y^2=49$

If the graphing calculator cannot draw the equation $x^2+y^2=49$

Find the value of $y$

Then draw the graph

  $\begin{array}{l}{x}^2+y^2=49\\ y=\pm \sqrt{49-x^2}\end{array}$

The graph of the equation is

  

(d)

To determine

To Solve: The equation for $y$ and explain why you need two equations to graph a circle.

Answer to Problem 57PPS

  $y=\pm \sqrt{4-{(x-2)}^2}-1$

Explanation of Solution

Given: ${(x-2)}^2+{(y+1)}^2=4$

Given: ${(x-2)}^2+{(y+1)}^2=4$

Solving

  $\begin{array}{l}$ {(x-2)}^2+{(y+1)}^2=4$y+1=\pm \sqrt{4-{(x-2)}^2}\\ y=\pm \sqrt{4-{(x-2)}^2}-1\end{array}$

Thus

  $y=\pm \sqrt{4-{(x-2)}^2}-1$

We need two equations to graph the circle because the equation of the circle is not a function.

(e)

To determine

To Describe: Do you think the equation in part (d) would be easier to draw on graph paper, pen or using graphing calculator?

Answer to Problem 57PPS

Graphing calculator

Explanation of Solution

Given: ${(x-2)}^2+{(y+1)}^2=4$

Given: ${(x-2)}^2+{(y+1)}^2=4$

  $\begin{array}{l}(h,k)=(2,-1)\\ r=4\end{array}$

It would be easier to draw the graph using the graphing calculator

Just plot the centers and radius.