Question

What happens as the foci of an ellipse move towards its vertices?

Answer 1

The FOC I adapts to the eclipse transforms

Answer 2

Answer with explanation:

An ellipse is the locus of all the points such that ,it's distance from two fixed point , known as focus (Focii, as there are two focus in an ellipse) is always constant which is equal to 2 p, where (p,0) and (-p,0) are vertices of focus.

Consider the equation of the ellipse

  $\frac{x^2}{a^2} +\frac{y^2}{b^2}=1$

having focus on major axis, and vertices where ellipse touches the axis are (a,0) , (-a,0) , (0,b) and (0, -b).

Coordinates of Focus, p = ( a e, 0) and (-a e, 0), where e is the eccentricity of ellipse.

Also,⇒ a²=b²+ p²

Suppose original ellipse has size S, having coordinates of focus (a e, 0) and (-a e, 0). Now , when foci of ellipse moves toward it's vertices the size of New Ellipse will be larger than Original ellipse.