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Question
Find the equation of the ellipse with foci at (± 5, 0) and x = `36/5` as one of the directrices.
Solution
We have ae = 5, `a/e = 36/5`
Which give a 2 = 36 or a = 6
Therefore, e = `5/6`.
Now `b = asqrt(1 - "e"^2)`
= `6sqrt(1 - 25/36)`
= `sqrt(11)`.
Thus, the equation of the ellipse is `x^2/36 + y^2/11` = 1.
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