Considering the ellipse with focal semidistance $$4$$ and cutting point with the axis $$OX$$ $$(5, 0)$$, calculate its eccentricity.
See development and solution
Development:
The focal semidistance is $$4$$ since $$F$$ is at $$4$$ from the center.
The biggest axis goes from $$-5$$ to $$5$$, therefore it measures $$10$$.
This way, the biggest semiaxis will be half, which is $$5$$.
The eccentricity will be: $$e=\dfrac{c}{a}=\dfrac{4}{5}$$.
Solution:
$$e=\dfrac{4}{5}$$