Find a rectangular-coordinate equation for the curve by eliminating the parameter. $x = t + 3 , y = \frac { t } { t + 3 }$
A) $y = \frac { x - 4 } { x }$

B) $y = \frac { x - 2 } { x }$

C) $y = \frac { x - 2 } { 3 x }$

D) $y = \frac { 2 x - 1 } { 2 x }$

E) none of these

Question

Find a rectangular-coordinate equation for the curve by eliminating the parameter. $x = t + 3 , y = \frac { t } { t + 3 }$
A) $y = \frac { x - 4 } { x }$

B) $y = \frac { x - 2 } { x }$

C) $y = \frac { x - 2 } { 3 x }$

D) $y = \frac { 2 x - 1 } { 2 x }$

E) none of these

Quizplus · Accepted Answer

To eliminate the parameter $t$, we express $t$ in terms of $x$ from the first equation: $t = x - 3$. Substituting this into the second equation gives $y = \frac{x - 3}{x}$, which does not match any of the provided options.

Find a Rectangular-Coordinate Equation for the Curve by Eliminating the Parameter