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 (a) `x y=1` (b) `y+x=2` (c) `y^2-x^2=4` (d) `y^2-x^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`.