Consider the surface parametrized by

G$($s$,$t$)=($:s$^(2)$cost$,$s$^(2)$sint$,$s:$),($s$,$t$)$in$[-3,3]\backslash$times $[0,2\backslash$pi $].^(2)$

$($a$)$ Find a parametrization of the tangent plane at the point $(1,0,-1).$

$($b$)$ Compute a vector normal to the surface at the point $(1,0,-1).$

$($c$)$ Find an equation for this surface of the form F$($x$,$y$,$z$)=0.$