Answer
Hyperbolic paraboloid
$z= y^{2}-x^{2}$
Work Step by Step
Given: $r=\lt s, t, t^{2}-s^{2}\gt$
Write the vector equation in its equivalent parametric equations:
$x=s$, $y= t$ and $z= t^{2}-s^{2}$
Solving the first two parametric equations yields:
$z= y^{2}-x^{2}$
which represents as a hyperbolic paraboloid.
