Find two sets of parametric equations for the given rectangular equation.
-$$y = x ^ { 2 } - 4$$
A) $x = t , y = t ^ { 2 } - 4 ; x = \sqrt { t } , y = t - 4 , t \geq 0$
B) $x = t , y = t ^ { 2 } - 4 ; x = \sqrt { t } , y = t + 4 , t \geq 0$
C) $x = - t , y = t ^ { 2 } + 4 ; x = \sqrt { t } , y = t - 4$
D) $x = - t , y = t ^ { 2 } - 4 ; x = \sqrt { t } , y = - t + 4 , t \geq 0$

Question

Quizplus · Accepted Answer

The correct parametric equations are those that can be derived directly from the given rectangular equation $y = x^2 - 4$. In choice A, both sets of parametric equations correctly represent the given rectangular equation. For the first set, $x = t$ directly translates to $y = t^2 - 4$ when substituted into the rectangular equation. For the second set, $x = \sqrt{t}$ translates to $y = t - 4$ when $x^2 = t$ is substituted into the rectangular equation, with the condition $t \geq 0$ ensuring $x = \sqrt{t}$ is real.

Find Two Sets of Parametric Equations for the Given Rectangular y=x2−4y = x ^ { 2 } - 4y=x2−4

Find Two Sets of Parametric Equations for the Given Rectangular $y = x ^ { 2 } - 4$