What are the effects when changing the values of $a$ and $b$?

Question

The question given is:

The general equations of three of the conic sections with their centres at the origin are given. Explore the effect of changing the values of $a$ and $b$.

I have been able to answer the parts regarding the parabola and ellipse, but I am stuck on how to answer the equation on the hyperbola.

$$\frac{x^2} {a^2}- \frac {y^2}{b^2} = 1$$

Answer 1

Hint:

Distance between the vertices and eccentricity would change. $a$ and $b$ are just measurement of semi-transverse and conjugate axis.