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Question
Find the eccentricity of an ellipse if the distance between its directrix is three times the distance between its foci
Solution
Let the equation of the ellipse be
`x^2/"a"^2 + y^2/"b"^2` = 1
It is given that,
distance between directrices is three times the distance between the foci.
∴ `(2"a")/"e"` = 3(2ae)
∴ 1 = 3e2
∴ e2 = `1/3`
∴ e = `1/sqrt(3)`. ...[∵ 0 < e < 1]
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