Question

In Problems 27-34, find two different parametric equations for each rectangular equation$x=y^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

Short answer

Two different Parametric equations are$x=tandy=t^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

Step-by-step solution

Step 1. Given Equation

$$\begin{gathered} x=y^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} \\ or \\ y=x^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.} \end{gathered}$$

Step 2. Solve for getting Parametric Equations

Let $x=twhere-\infty <t<\infty$

Then by putting the value $x$in the given equation, we get

$y=t^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}Where-\infty <t<\infty$