Q.

Let 0<θ<π2. If the eccentricity of the hyperbola x2cos2θy2sin2θ=1 is greater than 2 then the length of its latus rectum lies in the interval

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a

3,

b

1,32

c

2,3

d

32,2

answer is A.

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Detailed Solution

cos2θ+sin2θcos2θ>4

sec2θ>4

θ>π3

L.L=2sin2θcosθ

=2tanθ.sinθ

>23.32

>3

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