Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.
$\begin{array} { l }
x = t + 5 \
y = t ^ { 2 }
\end{array}$
A) $y = x ^ { 2 } + 10 x + 25$
B) $y = x ^ { 2 } - 10 x + 25$
C) $y = t + 5$
D) $y = x ^ { 2 }$
E) $y = t - 5$

Question

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. 
$\begin{array} { l } 
x = t + 5 \
y = t ^ { 2 }
\end{array}$ 
A) $y = x ^ { 2 } + 10 x + 25$
B) $y = x ^ { 2 } - 10 x + 25$
C) $y = t + 5$
D) $y = x ^ { 2 }$
E) $y = t - 5$

Quizplus · Accepted Answer

To eliminate the parameter $t$, solve the first equation for $t$: $t = x - 5$. Substitute $t$ in the second equation: $y = (x - 5)^2$, which simplifies to $y = x^2 - 10x + 25$.

Eliminate the Parameter and Write the Corresponding Rectangular Equation Whose x=t+5y=t2\begin{array} { l } x = t + 5 \\y = t ^ { 2 }\end{array}x=t+5y=t2​

Eliminate the Parameter and Write the Corresponding Rectangular Equation Whose $\begin{array} { l } x = t + 5 \\y = t ^ { 2 }\end{array}$