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Question

If for the ellipse x2a2+y2b2=1, the y-axis is the minor axis and the length of the latus rectum is one half of the length of its minor axis, then its eccentricity is


A

12

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B

12

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C

32

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D

34

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E

35

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Solution

The correct option is C

32


Explanation for the correct answer:

Given, the equation of the ellipse is,

x2a2+x2b2=1

given, the length of latus rectum = one half of the length of its minor axis.

Length of the latus rectum=2b2a

Length of minor axis=2b

According to the problem,

2b2a=12(2b)2b2a=bb=a2a=2b

Now, the eccentricity of ellipse is,

1-b2a2=1-b2(2b)2=1-b24b2=4b2-b24b2=3b24b2=32

Hence, option C is correct.


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