Chapter 11.1, Problem 2QR

To determine

The equation relating $x$ and $y$ .

Answer to Problem 2QR

Therequired answer is $y=2x^2-3$ .

Explanation of Solution

Given:

  $x=3t$  ...... (1)

  $y=54t^3-3$  ...... (2)

Calculation:

From equation (1)

  $\begin{array}{l}x=3t\\ t=\frac{x}{3}\end{array}$

From equation (2)

  $y=54t^3-3$

Substitute $\frac{x}{3}$ for $t$ in equation (2)

  $\begin{array}{l}y=54{\left(\frac{x}{3}\right)}^3-3\\ y=54\left(\frac{x^3}{27}\right)-3\\ y=2x^3-3\end{array}$

Conclusion:

Hence, the required answer is $y=2x^2-3$ .