Question

Consider the following parametric equations:x = V1 – 2 and y = 41 – 2==Step 1 of 2: Eliminate the parameter t. Please write your answer in simplest form solved for y.Answery =

Answer 1

Solution:

Given:

$\begin{gathered} x=\sqrt{t-2} \\ y=4t-2 \end{gathered}$$\begin{gathered} x=\sqrt{t-2} \\ Square\text{ both sides;} \\ x^2=t-2 \\ x^2+2=t \\ t=x^2+2 \end{gathered}$

Substitute the expression for t into y

$\begin{gathered} y=4t-2 \\ y=4(x^2+2)-2 \\ y=4x^2+8-2 \\ y=4x^2+6 \end{gathered}$

Therefore, in the simplest form,

$y=4x^2+6$