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## Q. 2.1

Find the equation of a line (or lines) tangent to the curve $x=e^{t}, y=e^{-t}$ at the point (1,1).

## Verified Solution

The point (1,1) is reached only when t=0. Then

$\frac{d y}{d x}=\frac{d\left(e^{-t}\right) / d t}{d\left(e^{t}\right) / d t}=-\left.\frac{e^{-t}}{e^{t}}\right|_{t=0}=-1$,

and the equation of the tangent line is

$\frac{y-1}{x-1}=-1, \quad \text { or } \quad y=-x+2$.