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Question

The equation to the hyperbola having its eccentricity 2 and the distance between its foci is 8, is,


A

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B

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C

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D

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Solution

The correct option is B


In the standard hyperbola,

x2a2 y2b2 = 1

Given that eccentricity,

e=2

Also distance between the foci is given by 2ae.

Given,

2ae=8

i.e.,ae=4

a=4e = 2

The lengths of transverse axis,conjugate axis and

the eccentricity are related by.

b2 = a2 (e21)

i.e.,b2=4.(41)

=12.

The required equation of hyperbola is,

x24 y212 = 1


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