Answer
$(0.909,-0.416,2)$ and $(-0.909,-0.416,-2)$
Work Step by Step
General form of parametric equation for $r(t)= (\sin^2 t+\cos^2 t)+t^2=5$ is:
$\sin^2 t+\cos^2 t=1$
We are given that the paraboloid equation $z=x^2+y^2$
$1+t^2=5$
This gives: $t^2=4$
and $ t= \pm 2$
Now, the value of $t$ for the point of intersection are;
$ \lt \sin (2), \cos (2), 2 \gt; \lt \sin (-2), \cos (-2), 2 \gt$
Point of intersection: $(0.909,-0.416,2); (-0.909,-0.416,-2)$