Question

Find the equation of the ellipse in standard form if: the distance between foci is 6 and the distance between directrices is

Answer 1

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

Distance between foci = 2ae 

Given, distance between foci = 6 

2ae = 6 

ae = 3

a = 3/e …….(i)

Distance between directrices = 2a/e

Given, distance between directrices = 50/3

The required equation of ellipse is \(\frac {x^2}{25}+\frac{y^2}{16}=1\)