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
4a² = 144
a² = 36
a = 6
2ae = 8
ae = 4
6.e = 4
e = 2/3
b² = a²(1 - e²)
= 36 (1 - 4/9)
36(5/8)
= 20

Equation of the ellipse is :-

(x²/36) + (y²/20) = 1