Find a set of parametric equations for the rectangular equation. $t = 2 - x$ $y = x ^ { 2 } + 5$
A) $x = - t + 2 , y = t ^ { 2 } + 4 t + 9$
B) $x = - t + 2 , y = t ^ { 2 } - 4 t - 9$
C) $x = t - 2 , y = t ^ { 2 } - 4 t + 9$
D) $x = - t + 2 , y = t ^ { 2 } - 4 t + 9$
E) $x = t - 2 , y = t ^ { 2 } - 4 t - 9$

Question

Find a set of parametric equations for the rectangular equation.  $t = 2 - x$ $y = x ^ { 2 } + 5$ 
A) $x = - t + 2 , y = t ^ { 2 } + 4 t + 9$
B) $x = - t + 2 , y = t ^ { 2 } - 4 t - 9$
C) $x = t - 2 , y = t ^ { 2 } - 4 t + 9$
D) $x = - t + 2 , y = t ^ { 2 } - 4 t + 9$
E) $x = t - 2 , y = t ^ { 2 } - 4 t - 9$

Quizplus · Accepted Answer

Given $t = 2 - x$, solving for $x$ gives $x = -t + 2$. Substituting $x = -t + 2$ into $y = x^2 + 5$ gives $y = (-t + 2)^2 + 5 = t^2 - 4t + 4 + 5 = t^2 - 4t + 9$.

Find a Set of Parametric Equations for the Rectangular Equation t=2−xt = 2 - xt=2−x

Find a Set of Parametric Equations for the Rectangular Equation $t = 2 - x$