Option 1. [tex]y = 3x^{2} +7[/tex] is obtained by eliminating the parameter.
Step-by-step explanation:
Step 1:
We have that [tex]x = \sqrt{t}[/tex] and [tex]y = 3t+7.[/tex]
Take [tex]x = \sqrt{t}[/tex] as equation 1.
Assume [tex]y = 3t+7[/tex] 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
[tex]x^{2} = (\sqrt{t})^{2} , x^{2} =t .[/tex]
So we have a value that can replace t, so we substitute this is equation 2.
[tex]y = 3t+7, x^{2} =t,[/tex] so
[tex]y = 3x^{2} +t[/tex] which is the first option.
