Chapter 9.4, Problem 48E

(a)

To determine

To calculate:To find the set of parametric equations to represent the given rectangular equation using $t=x$

Answer to Problem 48E

Parametric equations are

  $\begin{array}{l}x=t\\ y=\frac{1}{t^2}\end{array}$

Explanation of Solution

Given information: Rectangular equation is $y=\frac{1}{x^2}$

Calculation:

Rectangular equation is given as follows:

  $y=\frac{1}{x^2}$

Given polar equation is $t=x$

From this,

  $x=t$

Substitute $x=t$ in the rectangular equation

  $y=\frac{1}{t^2}$

Conclusion:

Hence, parametric equations are

  $\begin{array}{l}x=t\\ y=\frac{1}{t^2}\end{array}$

(b)

To determine

To calculate:To find the set of parametric equations to represent the given rectangular equation using $t=2-x$

Answer to Problem 48E

Parametric equations are

  $\begin{array}{l}x=2-t\\ y=\frac{1}{{\left(t-2\right)}^2}\end{array}$

Explanation of Solution

Given information: Rectangular equation is $y=\frac{1}{x^2}$

Calculation:

Rectangular equation is given as follows:

  $y=\frac{1}{x^2}$

Given polar equation is $t=2-x$

From this,

  $x=2-t$

Substitute $x=2-t$ in the rectangular equation

  $y=\frac{1}{{\left(t-2\right)}^2}$

Conclusion:

Hence, parametric equations are

  $\begin{array}{l}x=2-t\\ y=\frac{1}{{\left(t-2\right)}^2}\end{array}$