Chapter 10.7, Problem 12AYU

In Problems 7-26, graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.

$x=\sqrt{t}+4$, $y=\sqrt{t}-4$; $t\ge 0$

To determine

To find:

a. The rectangular equation of the curve.

Answer to Problem 12AYU

$x=y+8,\left|x-4\right|\ge 0$

Explanation of Solution

Given:

$x=\sqrt{t}+4,y=\sqrt{t}-4;t\ge 0$

Calculation:

$x=\sqrt{t}+4,y=\sqrt{t}-4;t\ge 0$

$x=y+4+4,t\ge 0$

$x=y+8,\left|x-4\right|\ge 0$

To determine

To graph:

b. $x=\sqrt{t}+4,y=\sqrt{t}-4;t\ge 0$, verify with the graph of rectangular equation of the curve.

Answer to Problem 12AYU

Explanation of Solution

Given:

$x=\sqrt{t}+4,y=\sqrt{t}-4;t\ge 0$

Graph:

The graph of $x=\sqrt{t}+4,y=\sqrt{t}-4;t\ge 0$ is plotted.

The graph of $x=y+8, \left(y+4\right)\ge 0$ is plotted.

Graph 1 represents the graph of $x=\sqrt{t}+4,y=\sqrt{t}-4;t\ge 0$ plotted in parametric mode and the orientation is shown.

The rectangular equation of the curve is calculated. Graph 2 represents the curve of the rectangular equation $x=y+8,\left|x-4\right|\ge 0$.

Both the equation represents the same graph and orientation. Hence it is verified.