Find a set of parametric equations for the rectangular equation. $\begin{array} { l }
t = 2 - x \
y = 1 - 6 x ^ { 2 }
\end{array}$
A) $x = - t + 2 , y = - 6 t ^ { 2 } + 24 t - 23$
B) $x = t + 2 , y = - 6 t ^ { 2 } + 24 t - 23$
C) $x = t - 2 , y = - 6 t ^ { 2 } + 24 t - 23$
D) $x = - t + 2 , y = - 6 t ^ { 2 } + 23 t - 24$
E) $x = t + 2 , y = - 24 t ^ { 2 } + 6 t + 23$

Question

Find a set of parametric equations for the rectangular equation.​ $\begin{array} { l } 
t = 2 - x \
y = 1 - 6 x ^ { 2 }
\end{array}$ ​​
A) $x = - t + 2 , y = - 6 t ^ { 2 } + 24 t - 23$
B) $x = t + 2 , y = - 6 t ^ { 2 } + 24 t - 23$
C) $x = t - 2 , y = - 6 t ^ { 2 } + 24 t - 23$
D) $x = - t + 2 , y = - 6 t ^ { 2 } + 23 t - 24$
E) $x = t + 2 , y = - 24 t ^ { 2 } + 6 t + 23$

Quizplus · Accepted Answer

Given $t = 2 - x$, solving for $x$ gives $x = 2 - t$. Substituting $x = 2 - t$ into $y = 1 - 6x^2$ gives $y = 1 - 6(2-t)^2$, which simplifies to $y = -6t^2 + 24t - 23$, matching option A.

Find a Set of Parametric Equations for the Rectangular Equation t=2−xy=1−6x2\begin{array} { l } t = 2 - x \\y = 1 - 6 x ^ { 2 }\end{array}t=2−xy=1−6x2​

Find a Set of Parametric Equations for the Rectangular Equation $\begin{array} { l } t = 2 - x \\y = 1 - 6 x ^ { 2 }\end{array}$