Chapter 1, Problem 12RQ

To determine

To find: Whether the given statement is true or false.

Answer to Problem 12RQ

The given statement is false.

Explanation of Solution

Given:

The given statement is $x=t^2$ , $y=t^4$ have the same graph as $x=t^3$ and $y=t^6$ .

Calculation:

Consider the given parametric equations,

  $\begin{array}{l}x=t^2\\ y=t^4\end{array}$

For $t=-1$

  $\begin{array}{l}x=1\\ y=1\end{array}$

Consider the given parametric equations,

  $\begin{array}{l}x=t^3\\ y=t^6\end{array}$

For $t=-1$

  $\begin{array}{l}x=-1\\ y=1\end{array}$

As the points obtained are different therefore the graph for the two sets of parametric equations is not same.

Thus, the given statement is false.