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) $y = t - 5$
B) $y = x ^ { 2 } + 10 x + 25$
C) $y = x ^ { 2 }$
D) $y = x ^ { 2 } - 10 x + 25$
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) $y = t - 5$
B) $y = x ^ { 2 } + 10 x + 25$
C) $y = x ^ { 2 }$
D) $y = x ^ { 2 } - 10 x + 25$
E) $y = t + 5$

Quizplus · Accepted Answer

To eliminate the parameter, we can solve for the parameter $t$ in the first equation:

$$t=x-5$$

We can then substitute this expression for $t$ into the second equation:

$$y=(x-5)^2$$

Expanding the square, we get:

$$y=x^2-10x+25$$

This is the rectangular equation that corresponds to the given parametric equation. The correct choice is (D).

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 $\begin{array} { l } x = t + 5 \\y = t ^ { 2 }\end{array}$