find the equation of ellipse .the distance between foci is 8 unit and the distance between directrix is 18 units.

Distance between two foci = ae – (- ae) = 2ae =8

Distance between two directrices =a/e – (-a/e) = 2a/e =18

2ae .2a/e = 8 x 18

4a^{2} = 144

a^{2} = 36

a = 6

2ae = 8

ae = 4

6.e = 4

e = 2/3

b^{2} = a^{2}(1 - e^{2})

= 36 (1 - 4/9)

36(5/8)

= 20

Equation of the ellipse is :-

(x^{2}/36) + (y^{2}/20) = 1