Question 3

Given the parametric equations below, eliminate the parameter $t$ to obtain an equation for $y$ as a function of $x$
\[
\begin{array}{l}
\left\{\begin{array}{l}
x(t)=4 \sqrt{t} \\
y(t)=8 t+5
\end{array}\right. \\
y(x)=
\end{array}
\]

Answer

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Answer

$\boxed{y(x) = \frac{x^2}{2} + 5}$

Steps

Step 1 ：Given the parametric equations $x(t)=4 \sqrt{t}$ and $y(t)=8 t+5$

Step 2 ：Express $t$ in terms of $x$ from the equation $x(t)=4 \sqrt{t}$, we get $t = \frac{x^2}{16}$

Step 3 ：Substitute $t$ in the equation for $y(t)$ with $\frac{x^2}{16}$ to get $y(x)$

Step 4 ：Simplify the equation to get the final answer

Step 5 ：$\boxed{y(x) = \frac{x^2}{2} + 5}$