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Q.

Let 0<θ<π2, If the eccentricity of the hyperbola x2cos2θ-y2sin2θ=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 B.

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Detailed Solution

Given  hyperbola x2cos2θ-y2sin2θ=1 Given e>2e2>4                        cos2θ+sin2θcos2θ>4                          sec2θ>4                     1+tan2θ>4                     tan2θ>3                     tanθ>3                     θ>π3                     θπ3, π2 Now L.L.R=2sin2θcosθ                     =2(1-cos2θ)cosθ L.L.R=2(secθ-cosθ) If θ=π3L.L.R=22-12=3 If θ=π2L.L.R=  L.L.R. lies in (3, )

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