Answer
$(0.909,-0.416,2)$ and $(-0.909,-0.416,-2)$
Work Step by Step
Write the parametric equations from the given problem $r(t)= (\sin^2 t+\cos^2 t)+t^2=5$ as follows:
That is, $\sin^2 t+\cos^2 t=1$
When we plug these parametric equations in to the given paraboloid equation:
$z=x^2+y^2 \implies 1+t^2=5$
and $t^2=4; t= \pm 2$
Thus we have the point of intersection $ \lt \sin 2, \cos 2, 2 \gt$
Re-arrange as:
$ \lt \sin (-2), \cos (-2), 2 \gt$
Hence, we get $(0.909,-0.416,2)$ and $(-0.909,-0.416,-2)$