Find a rectangular-coordinate equation for the curve by eliminating the parameter. $x = t + 2 , y = \frac { t } { t + 2 }$

A) $y = \frac { x - 4 } { x }$

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

C) $y = \frac { x - 2 } { 4 x }$

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. $x = t + 2 , y = \frac { t } { t + 2 }$

A) $y = \frac { x - 4 } { x }$

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

C) $y = \frac { x - 2 } { 4 x }$

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

E) none of these

Quizplus · Accepted Answer

To eliminate the parameter t, we isolate t in the x-equation, $t=x-2$ and substitute it into the y-equation: $y = \frac{x-2}{x-2+2}=\frac{x-2}{x}$. Simplifying this expression, we get $y = \frac{x-2}{x}$, which is option B.

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