The locus of the moving point whose coordinates are given by `(e^t+e^(-t),e^t-e^(-t))` where `t` is a parameter, is `x y=1` (b) `x+y=2` `x^2-y^2=4` (d) `x^2-y^2=2`

Options

A. `xy=1`
B. `x+y=2`
C. `x^2-y^2=4`
D. `x^2-y^2=2`

Answer

C

Explanation

Let `(e^t+e^(-t),e^(t)-e^(-t))-=(h,k)`
or `h=e^t+e^(-t) and k=e^(t)-e^(-t)`
Squareing and subtracing we get
`h^2-k^2=(e^t+e^(-t))^2-(e^(t)-e^(-t))^2=4`
Therefore,the locus is `x^2-y^2=4`.