$($a$)$ Eliminate the parameter to find a Cartesian equation of the parametric curve: $x(t)=\sqrt[\phantom{2}]{t},y(t)=\frac{1}{t}$

$($b$)$ Sketch the curve and describe the motion of a particle for $t>0.$

$($c$)$ Find an equation of the line tangent to the curve at $t=4$ and add it to the graph.

$x(t)=\sqrt[\phantom{2}]{t}$

$y(t)=\frac{1}{t}$