Question

Eliminate the parameter t. Find rectangular equation for the plane curve defined by the parametric equations

Answer 1

For this problem, we are given the value of x in the function of t, and the value of y in the function of t. We need to represent y in the function of f.

The first step is to isolate t on the x equation:

$\begin{gathered} x=\sqrt{t}\\ \\ x^2=t\\ \\ t=x^2 \end{gathered}$

Then we need to replace the expression for t on the right side of the function for y.

$y=2x^2+4$

The correct answer is the third one. The interval get decreased in half, because of the relation between x and t.