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Question

If the length of the major axis of an ellipse is 178 times the length of the minor axis, then the eccentricity of the ellipse is


A

817

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B

1517

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C

917

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D

2217

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E

1317

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Solution

The correct option is B

1517


Explanation for the correct option:

Let us assume the equation of the ellipse is x2a2+y2b2=1,a>b.

The length of the major axis can be given by 2a.

The length of the major axis can be given by 2b.

Thus, 2a=178×2b

ba=817.

Therefore the eccentricity of the ellipse can be given by, e=1-ba2

Put ba=817.

e=1-8172e=1-64289e=289-64289e=225289e=1517

Hence, option (B) is the correct answer.


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