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Question

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is___ .

A
43
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B
43
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C
23
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D
3
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Solution

The correct option is C 23
Let the hyperbola be x2a2y2b2=1
We have , 2b2a=8 and 2b=ae
b2=4a and 2b=ae
Consider, 2b=ae4b2=a2e24a2(e21)=a2e24e24=e23e2=4e=23

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