How do I prevent Animate from creating jagged curves?

Question

I have the following command:

Animate[
  ContourPlot[x^2 - a*y^2 == 1, {x, -5, 5}, {y, -5, 5}], 
  {a, -3, 3}, 
  DisplayAllSteps -> True]

I am trying to get an intuition for how a curve described by $x^2-a\cdot y^2 =1$ changes as $a$ changes.

However the above animate command creates a very jagged curve, making it impossible to get a feeling for whats going on. only when I pause the animation does the curve become smooth after a while, and this takes about a second. (the same problem with the manipulate command).

Here is what I get in the animation:

Only after I pause it, and wait for a second, does it become what it's supposed to look like:

My question is: How do I make the curve smooth during animation?

I prefer a smooth curve over fast processing time.