Answer
Hyperbolic paraboloid
Work Step by Step
The equation
$$ z=3x^2-7y^2$$ can be rewritten as follows
$$
z=\left(\frac{x}{1/\sqrt 3}\right)^{2}-\left(\frac{y}{1/\sqrt{7}}\right)^{2}
$$ which is an equation of a hyperbolic paraboloid with $ a=1/\sqrt{ 3}, b=1/\sqrt{7}$ (see equations on page 691).
