Question

Consider the following parametric equations:x = V1 – 2 and y = 1 + 3Step 1 of 2: Eliminate the parameter t. Please write your answer in simplest form solved for y.

Answer 1

The equations are given below as

`\begin{gathered} x=√(t-2)........(1) \\ y=t+3......(2) \end{gathered}`

Step 1:

Make t the subject of the formula from equation (1)

`\begin{gathered} x=√(t-2) \\ square\text{ both sides} \\ x^2=(√(t-2)^2) \\ x^2=t-2 \\ add\text{ 2 to both sides, we will have} \\ x^2+2=t-2+2 \\ t=x^2+2.....(2) \end{gathered}`

Step 2:

Substitute the equation (3) in equation (2)\

`\begin{gathered} y=t+3......(3) \\ t=x^2+2 \\ y=x^2+2+3 \\ y=x^2+5 \end{gathered}`

Hence,

The final equation for y after eliminating t is

`y=x^2+5`