Consider the parametric equations $x = 5 \sqrt { t }$ and $y = 2 + 7 t$. Find the rectangular equation by eliminating the parameter.
A) $y = \frac { 7 } { 25 } x ^ { 2 } + \frac { 2 } { 25 }$
B) $y = 175 x ^ { 2 } + 2$
C) $y = \frac { 1 } { 25 } x ^ { 2 } - \frac { 2 } { 7 }$
D) $y = \frac { 7 } { 25 } x ^ { 2 } + 2$
E) $y = \frac { 1 } { 175 } x ^ { 2 } + 14$

Question

Quizplus · Accepted Answer

To eliminate the parameter $t$, we solve the first equation for $t$: $t = \frac{x^2}{25}$. Substituting this into the second equation gives $y = 2 + 7(\frac{x^2}{25})$, which simplifies to $y = \frac{7}{25}x^2 + 2$.

Consider the Parametric Equations x=5tx = 5 \sqrt { t }x=5t​

Consider the Parametric Equations $x = 5 \sqrt { t }$