Eliminate the parameter.
-$$x = \frac { 1 } { 4 } t , y = 2 t ^ { 3 } - 4$$
A) $y = \frac { 1 } { 32 } t ^ { 3 } - 4$
B) $y = 128 x - 4$
C) $y = 128 x ^ { 3 } - 4$
D) $y = 8 x ^ { 3 } - 4$

Question

Quizplus · Accepted Answer

To eliminate the parameter $t$, we solve the first equation for $t$ and then substitute into the second equation. From $x = \frac{1}{4}t$, we get $t = 4x$. Substituting $t = 4x$ into $y = 2t^3 - 4$, we get $y = 2(4x)^3 - 4 = 128x^3 - 4$, which matches choice C.

Eliminate the Parameter x=14t,y=2t3−4x = \frac { 1 } { 4 } t , y = 2 t ^ { 3 } - 4x=41​t,y=2t3−4

Eliminate the Parameter $x = \frac { 1 } { 4 } t , y = 2 t ^ { 3 } - 4$