You are given the parametric equations $$x=te^t,\;\;y=te^{-t}.$$

(a) Use calculus to find the Cartesian coordinates of the highest point on the parametric curve.

$(x, y) =$ (,)

(b) Use calculus to find the Cartesian coordinates of the leftmost point on the parametric curve.

$(x, y) =$ (,)

(c) Find the horizontal asymptote for this curve.

$y =$

(d) Find the vertical asymptote for this curve.

$x =$