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Question

Find the eccentricity of the hyperbola, the length of whose conjugate axis is34 of the length of transverse asxis.

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Solution

Let 2a and 2b be the transverse and conjugate axes and e be the eccentricit.

Then,

The length of conjugate aaxis=34[length of transverse axis]

2b=34×(2a)

ba=34

b2a2=916

Now,using the relation

e=1+b2a2

=1+916

=2516

=54

Hence,e=54


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