For example, how would I find the parametric equations for (x^2)/(25) + (y^2)/(81) = 1
An ellipse is really just a stretched circle right?
Well the most common parameterization for a circle is
$\displaystyle x=a\cos(t)$
$\displaystyle y=a\sin(t)$
where "a" is the radius of the circle
So if we wanna stretch it, we look at your equation. The biggest value that x takes on is 5 and the biggest value of y is 9
So the radii are $\displaystyle \sqrt{5}$ and 3
So this time we just make the parameterization
$\displaystyle x=a\cos(t)$
$\displaystyle y=b\sin(t)$
with $\displaystyle a=5$ and $\displaystyle b=9$