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Question
Find the equation of the ellipse in the cases given below:
Length of latus rectum 8, eccentricity = `3/5` centre (0, 0) and major axis on x-axis
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Solution
e = `3/5`
Latus rectum `(2"b"^2)/"a"` = 8
b2 = `"a"^2(1 -"e"^2)`
4a = `"a"^2 (1 - 9/25)`
4 = `"a"(16/25)`
⇒ `25/4` = a
a2 = `625/16`
∴ b2 = 4a
= `4(25/4)` = 25
∴ Equation of Ellipse `x^2/"a"^2 + y^2/"b"^2` = 1
⇒ `(16x^2)/625 + y^2/25` = 1
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