Calc Vertice Problem: Finding the Closest Point in an Ellipse to a Focus

[flyingpig]

Homework Statement

One vertice is the closest point to a focus in an ellipse. For instance take

$$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ with a > b > 0 and one focus at (c,0) and one vertice at (a,0), is (a,0) the closest point on the ellipse to the focus (c,0)?


2. The attempt at a solution

This is true right?

 

[HallsofIvy]

Yes, that is true. And the other vertex, (-a, 0) is the point farthest from the focus.

By the way, the singular of "verices" is "vertex", not "vertice".