Which set of parametric equations represents the graph of the following rectangular equation using $t = 6 - x$ ?
$$y = x ^ { 2 } + 9$$
A)
$$\begin{array} { l }
x = t + 6 \
y = ( t + 6 ) ^ { 2 } - 9
\end{array}$$
B)
$$\begin{array} { l }
x = t - 6 \
y = ( t - 6 ) ^ { 2 } - 9
\end{array}$$
C)
$$\begin{array} { l }
x = t - 6 \
y = ( t - 6 ) ^ { 2 } + 9
\end{array}$$
D)
$$\begin{array} { l }
x = 6 + t \
y = ( 6 + t ) ^ { 2 } + 9
\end{array}$$
E)
$$\begin{array} { l }
x = 6 - t \
y = ( 6 - t ) ^ { 2 } + 9
\end{array}$$

Question

Which set of parametric equations represents the graph of the following rectangular equation using $t = 6 - x$ ?
$$y = x ^ { 2 } + 9$$
A)
$$\begin{array} { l } 
x = t + 6 \
y = ( t + 6 ) ^ { 2 } - 9
\end{array}$$
B)
$$\begin{array} { l } 
x = t - 6 \
y = ( t - 6 ) ^ { 2 } - 9
\end{array}$$
C)
$$\begin{array} { l } 
x = t - 6 \
y = ( t - 6 ) ^ { 2 } + 9
\end{array}$$
D)
$$\begin{array} { l } 
x = 6 + t \
y = ( 6 + t ) ^ { 2 } + 9
\end{array}$$
E)
$$\begin{array} { l } 
x = 6 - t \
y = ( 6 - t ) ^ { 2 } + 9
\end{array}$$

Quizplus · Accepted Answer

To use $t = 6 - x$, we need to solve for $x$ in terms of $t$, which gives us $x = 6 - t$. Then, substituting this into the rectangular equation, we get $y = (6-t)^2+9$. Thus, the correct set of parametric equations is:
$$\begin{aligned} 
x &= 6-t \
y &= (6-t)^2+9
\end{aligned}$$
which corresponds to choice E.

Which Set of Parametric Equations Represents the Graph of the Following