Find the equation of an ellipse, the distance between the foci is 8 units and the distance between the directrices is 18 units.
Given that we need to find the equation of the ellipse whose distance between the foci is 8 units and distance between the directrices is 18 units.
We know that the distance between the foci is 2ae.
⇒ 2ae = 8
⇒ ae = 4 ..... - (1)
We know that the distance between the directrices is 
.
⇒ 
⇒ 
..... - (2)
(1)×(2)
⇒ 
⇒ a2 = 36 .... (3)
⇒ a = 6
We know that eccentricity of an ellipse is 
⇒ 
⇒ 36 - b2 = 16
⇒ b2 = 20 ..... (4)
The equation of the ellipse is,
⇒ 
⇒ 
⇒ 5x2 + 9y2 = 180
∴ The equation of the ellipse is 5x2 + 9y2 = 180.
16