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Question
Find the equation of an ellipse whose latus rectum is 8 and eccentricity is `1/3`
Solution
`(2b^2)/a = 8`
`b^2 = 4a`
`e = 1/3`
`b^2 = a^2(1-e^2)`
`:. 4a = a^2 (1-(1/3)^2)`
`4a = a^2 (8/9)`
`9/2 = a`
`a^2 = 81/4`
`b^2 = 4a = 4 xx 1/2 = 18`
Equation of ellipse
`x^2/a^2 + y^2/b^2 = 1`
`(4x^2)/81 + y^2/18 = 1`
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