LA$4.$ Consider the curve $r(t)=($:$sintcost,co{s}^{2}t,cost$:$),$tin$[0,2].$

$($a$)$ Find the curvature at the point $P=(\frac{1}{2},\frac{1}{2},\frac{\sqrt[\phantom{2}]{2}}{2})$

$($b$)$ Show that the curve lies on a cone and also on a sphere $($specify the center and the radius of the sphere$).$