Question

In Problems 27–34, find two different parametric equations for each rectangular equation$y=x^3$

Short answer

Two different parametric equations are $y=t^{3}andy=t$

Step-by-step solution

Step 1. Given Equation 

$y=x^3$

Step 2. Solve for getting parametric equations .

let us assume that $x=t$

then putting the value of x in given equation we get $y=t^3$$-\infty \le t\le \infty$---------(1)

again solving given equation for x

we get $x=y^{\frac{1}{3}}$

Now again let us assume that $x=t^{\frac{1}{3}}$

we get$y={\left(t^{\frac{1}{3}}\right)}^3=t$$-\infty \le t\le \infty$---(2)