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Question

# Arrange the eccentricities of the following ellipses in particular order. A- Ellipse whose Latus rectum is half of its major axis. B- Ellipse whose distance between the foci is equal to the distance between a focus and one end of minor axis C- Ellipse whose major axis is double the minor axis. D- Ellipse whose distance between the foci is 6 and the length of minor axis is 8.

A

(A)=(C)>(D)>(B)
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B

(A)=(C)<(D)<(B)
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C

(A)>(C)>(D)>(B)
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D
none of these
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Solution

## The correct option is B (A)=(C)<(D)<(B)A) Latusrectum is 2b2a=a2Using e=√1−b2a2 and above relation we get e=√32B) Distance between foci is given by 2ae and this is equal to a−aeThis gives e=13C) e=√1−b2a2, now if a=2b then e=√32D) Given 2a=8 and 2ae=6 we get e=34(A)=(C)>(D)>(B)

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