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Question
Find the equation of the ellipse in standard form if the minor axis is 16 and eccentricity is `1/3`.
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Solution
Let the equation of the ellipse be
`x^2/"a"^2 + y^2/"b"^2` = 1 ...(1)
Then minor axis = 2b = 16
∴ b = 8
Also, eccentricity = e = `1/3`
∴ b2 = a2(1 – e2) gives
(8)2 = `"a"^2(1 - 1/9)`
∴ 64 = `(8"a"^2)/9`
∴ a2 = 72
∴ from (1), the equation of the required ellipse is
`x^2/72 + y^2/64` = 1.
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