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

Starting with the given parametric equations, we can eliminate the parameter $t$ by isolating $t$ in the equation $x=5\sqrt{t}$, squaring both sides to get $t=\frac{x^2}{25}$, and substituting into the equation $y=2+7t$ to get $y=2+\frac{7x^2}{25}$. Simplifying this expression, we get $y=\frac{7}{25}x^2+2$, which is the rectangular equation in standard form. Thus, the answer is $\boxed{	extbf{(D)}}$.

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

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