Question

Find the eccentricity of an ellipse if the distance between its directrices is three times the distance between its foci.

Answer 1

Let the required equation of ellipse be \(\frac {x^2}{a^2} + \frac {y^2}{b^2} = 1\), 

It is given that, distance between directrices is three times the distance between the foci

∴ 2a/e = 3(2ae)

∴ 1 = 3e²

e² = 1/3

∴ e = 1/√3…..[∵ 0 < e < 1]