Let the product of the focal distances of the point
$$ \left( \sqrt{3}, \frac{1}{2} \right) $$
on the ellipse
$$ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \quad (a > b), $$
be $ \frac{7}{4} $.
Then the absolute difference of the eccentricities of two such ellipses is: