Eliminate the parameter in the equations $x = t ^ { 2 } , y = t ^ { 4 }$
A) $y = x ^ { 2 } \text { for } x \geq 0$
B) $y = \sqrt { x } \text { for } x \geq 0$
C) $y = 2 x ^ { 2 } \text { for } x \geq 0$
D) $y = \sqrt { 2 x } \text { for } x \geq 0$
E) $y = 2 \sqrt { x } \text { for } x \geq 0$
F) $y = x ^ { 2 } / 2 \text { for } x \geq 0$
G) $y = \sqrt { x } / 2 \text { for } x \geq 0$
H) $y = \sqrt { x / 2 } \text { for } x \geq 0$

Question

Eliminate the parameter in the equations $x = t ^ { 2 } , y = t ^ { 4 }$ 
A) $y = x ^ { 2 } \text { for } x \geq 0$ 
B) $y = \sqrt { x } \text { for } x \geq 0$ 
C) $y = 2 x ^ { 2 } \text { for } x \geq 0$ 
D) $y = \sqrt { 2 x } \text { for } x \geq 0$ 
E) $y = 2 \sqrt { x } \text { for } x \geq 0$ 
F) $y = x ^ { 2 } / 2 \text { for } x \geq 0$ 
G) $y = \sqrt { x } / 2 \text { for } x \geq 0$ 
H) $y = \sqrt { x / 2 } \text { for } x \geq 0$

Quizplus · Accepted Answer

Given $x = t^2$, solving for $t$ gives $t = \sqrt{x}$ (considering $t \geq 0$ since $x \geq 0$). Substituting $t = \sqrt{x}$ into $y = t^4$ gives $y = (\sqrt{x})^4 = x^2$, hence $y = x^2$ for $x \geq 0$.

Eliminate the Parameter in the Equations x=t2,y=t4x = t ^ { 2 } , y = t ^ { 4 }x=t2,y=t4

Eliminate the Parameter in the Equations $x = t ^ { 2 } , y = t ^ { 4 }$