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Question
Find the equation of the ellipse in standard form if the length of major axis 10 and the distance between foci is 8
Solution
Let the equation of the ellipse be
`x^2/"a"^2 + y^2/"b"^2` = 1 ...(1)
Then length of major axis = 2a = 10
∴ a = 5
Also, distance between foci = 2ae = 8
∴ 2 × 5 × e = 8
∴ e = `4/5`
∴ b2 = `"a"^2(1 - "e"^2)`
= `5^2 [1 - (4/5)^2]`
= `25(1 - 16/25)`
= 9
∴ from (1), the equation of the required ellipse is `x^2/25 + y^2/9` = 1.
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