quite new in using this platform so I hope I'm doing it the right way.
I'm taking Pre-Calculus right now, and I'm trying to understand how some equations affect the resulting plot. As far as I understand in a hyperbolic paraboloid the horizontal traces are hyperbolas and the vertical traces are parabolas, so, given the equation:
$$ z = \frac{x^2}{a^2} - \frac{y^2}{b^2} + k $$
$k$ represents the displacement in the $z$-axis, but I quite don't get it when talking about $a$ and $b$, what's the effect when they are changed? What if $a$ is greater than $b$ or $b$ greater than $a$?
Thank you very much in advance.