Question

Find the eccentricity of an ellipse if the perpendicular drawn from the center of the ellipse to its directrix is divided in half by the vertex.

Answer 1

Solution-

We know that

For a horizontal ellipse centre at origin , the directrix is at x = ±a/e

It implies

Eccentricity =e = |a/x|

Ecentricity = e =

Distance between centre and vertex / perpendicular distance drawn from the centre of the ellipse.

Since the perpendicular drawn from the center of the ellipse to its directrix is divided in half by the vertex.

It means distance between vertex and centre/perpendicular distance from the centre of the vertex = 1/2

So, we can say that ecentricity e = 1/2

This is valid for any ellipse (either Vertical or not centre at origin).

Hence, here ecentricity of the ellipse is 1/2.