Find a rectangular equation for the plane curve defined by the parametric equations.
-$$x = t - 3 , y = t ^ { 2 } + 5$$
A) $y = x ^ { 2 } + 6 x + 14$
B) $y = x ^ { 2 } - 14$
C) $y = x ^ { 2 } + 14$
D) $y = x ^ { 2 } - 6 x - 14$

Question

Quizplus · Accepted Answer

To find the rectangular equation, solve one of the parametric equations for $t$ and substitute into the other. From $x = t - 3$, we get $t = x + 3$. Substituting $t = x + 3$ into $y = t^2 + 5$, we get $y = (x + 3)^2 + 5 = x^2 + 6x + 9 + 5 = x^2 + 6x + 14$.

Find a Rectangular Equation for the Plane Curve Defined by the Parametric