Chapter 1.5, Problem 4E

Solution

To find: The $\left(x,y\right)$ pair for the value of the parameter.

The required value of $\left(x,y\right)$ pair is $\left(5,-1/8\right)$ .

Given data: The parametric values of x and y are $x=\left|t+3\right|$ , $y=\frac{1}{t}$ and $t=-8$ .

Method/Formula used:

Substitute value of t in the expressions for x and y .

The absolute value $\left|\alpha +3\right|=-\left(\alpha +3\right),t<-3$

Calculation:

The parametric values of x and y are $x=\left|t+3\right|$ , $y=\frac{1}{t}$ and $t=-8$ .

The coordinate pair $\left(x,y\right)$ is equivalent to pair $\left(x=\left|t+3\right|,y=\frac{1}{t}\right)$ can be written as,

  $\left.\begin{array}{c}\left(x,y\right)\equiv \left(\left|t+3\right|,\frac{1}{t}\right)\\ \equiv \left(-\left(t+3\right),\frac{1}{t}\right),t<3\end{array}\right\}$ … (1)

Substitute -8 for $t$ on the right of result (1),

  $\begin{array}{c}\left(x,y\right)\equiv \left(-\left(-8+3\right),\frac{1}{-8}\right)\\ \equiv \left(-\left(-5\right),-1/8\right)\\ \equiv \left(5,-1/8\right)\end{array}$

Thus, the $\left(x,y\right)$ pair for $t=-8$ is $\left(5,-1/8\right)$.