The Rectangular Equation of the Plane Curve, with Parametric Equations $x ( t ) = e ^ { - t } + 1 , y ( t ) = e ^ { 2 t }$

Multiple Choice

The rectangular equation of the plane curve, with parametric equations $x ( t ) = e ^ { - t } + 1 , y ( t ) = e ^ { 2 t }$ with $t \in ( - \infty , \infty ) ,$ is

A) $y = \frac { 1 } { 1 - x ^ { 2 } }$
B) $y = \frac { 1 } { x ^ { 2 } - 1 }$
C) $y = \frac { 1 } { ( x - 1 ) ^ { 2 } }$
D) $y = \frac { 1 } { ( x + 1 ) ^ { 2 } }$
E) $y = \frac { 1 } { x ^ { 2 } + 1 }$