Question

Eliminate the parameter

Answer 1

Option 1. $y = 3x^{2} +7$ is obtained by eliminating the parameter.

Step-by-step explanation:

Step 1:

We have that $x = \sqrt{t}$ and $y = 3t+7.$

Take $x = \sqrt{t}$ as equation 1.

Assume $y = 3t+7$ is equation 2.

We need to determine a value that is equivalent to t so it can be substituted in equation 2.

Step 2:

If we square equation 1, we get

$x^{2} = (\sqrt{t})^{2} , x^{2} =t .$

So we have a value that can replace t, so we substitute this is equation 2.

$y = 3t+7, x^{2} =t,$ so

$y = 3x^{2} +t$ which is the first option.