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Question
Find the distance between the directrices of the ellipse `x^2/36 + y^2/20` = 1
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Solution
Given equation of ellipse is `x^2/36 + y^2/20` = 1
Here a2 = 36
⇒ a = 6
b2 = 20
⇒ b = `2sqrt(3)`
We know that b2 = a2(1 – e2)
⇒ 20 = 36(1 – e2)
⇒ 1 – e2 = `20/36`
⇒ e2 = `1 - 20/36 = 16/36`
⇒ e = `4/6 = 2/3`
Now distance between the directrices is `a/e - (a/e)`
= `a/e + a/e = (2a)/`
= `2 xx 6/(2/3)`
= `2 xx 6 xx 3/2`
= 18
Hence, the required distance = 18.
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