Question

The rectangular equation of the curve given parametrically by x=1+e^-t and y=1+e^t is
(a) y=2-x (b) y=x (c) y=1/x (d) y=x/(x-1)

Answer 1

d

Answer 2

\[
y-1=e^t\\
x-1 =e^{-t}\\
y-1=\frac{1}{x-1}\\
y=\frac{x}{x-1}
\]

Answer 3

care to explain the jump from y−1=1/x−1 to the answer?

Answer 4

\[y-1 = \frac 1{x-1}\\
y =1+ \frac 1{x-1}\\
y= \frac {(x-1)+1}
{x-1} \\
y=\frac {x}
{x-1} \\\]