Find a set of parametric equations for the rectangular equation. $t = 4 - x$ $y = \frac { 1 } { x }$
A) $x = 4 - t , y = \frac { - 1 } { ( t + 4 ) }$
B) $x = 4 - t , y = \frac { - 1 } { ( - t - 4 ) }$
C) $x = 4 - t , y = \frac { - 1 } { ( t - 4 ) }$
D) $x = 4 + t , y = \frac { - 1 } { ( t - 8 ) }$
E) $x = 8 - t , y = \frac { - 1 } { ( t - 4 ) }$

Question

Find a set of parametric equations for the rectangular equation.  $t = 4 - x$ $y = \frac { 1 } { x }$ 
A) $x = 4 - t , y = \frac { - 1 } { ( t + 4 ) }$
B) $x = 4 - t , y = \frac { - 1 } { ( - t - 4 ) }$
C) $x = 4 - t , y = \frac { - 1 } { ( t - 4 ) }$
D) $x = 4 + t , y = \frac { - 1 } { ( t - 8 ) }$
E) $x = 8 - t , y = \frac { - 1 } { ( t - 4 ) }$

Quizplus · Accepted Answer

The given equation $t = 4 - x$ implies $x = 4 - t$. Substituting $x = 4 - t$ into $y = \frac{1}{x}$ gives $y = \frac{1}{4 - t}$, which matches option C.

Find a Set of Parametric Equations for the Rectangular Equation t=4−xt = 4 - xt=4−x

Find a Set of Parametric Equations for the Rectangular Equation $t = 4 - x$