Problems from Study of the ellipse

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:

$$e=\dfrac{4}{5}$$

Hide solution and development
View theory