Find the equation of an ellipse the distance between the foci is 8 units and the distance between the directrices is 18 units.

Explanation

distance between foci is 8 units.

`2 a e=8 . . .(1)`

distance between directrices is 18 units.

`frac{2 a}{e}=18 . .` (2)

Comparing eqs. (1) and (2), we get :

`e=frac{8}{2 a}`

Substituting the value of e in eq. (2)

`frac{2 a}{frac{8}{2 a}}=18 `

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