I have 2 parametric ellipses, both represented using the standard parametric equation of an ellipse:
$$x = h + a \cos t $$ $$y = k + b \sin t $$
Lets say that the ellipses are cut-off at (see diagram)
$$ t = t1_{e1}, t1_{e2}, t2_{e1}, t2_{e2} $$
and also assuming the cut is a straight line.
What would the condition to test whether a point lies in the shaded (green) region?
The equation of the ellipse can be rewritten as:
$$\frac {(x-h)^2}{a^2} + \frac {(y-k)^2}{b^2} = 1$$
So given a test point $(x,y)$,
You need $\frac {(x-h_1)^2}{a_1^2} + \frac {(y-k_1)^2}{b_1^2} < 1$
and you need $\frac {(x-h_2)^2}{a_2^2} + \frac {(y-k_2)^2}{b_2^2} > 1$
... for it to lie between the two ellipses.