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

Quizplus · Accepted Answer

To eliminate the parameter, we need to solve for the parameter (t) in one equation and then substitute that into the other equation.

From the first equation, we get t = x - 2.

Substituting t = x - 2 into the second equation, we get y = (x-2)/(x-2+2) = (x-2)/x.

Simplifying this equation, we get y = (x/x) - (2/x) = 1 - 2/x.
Therefore, y = (x-2)/x, which matches choice (B).

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