Let $0 < \theta < {\pi \over 2}$. If the eccentricity of the hyperbola ${{{x^2}} \over {{{\cos }^2}\theta }} - {{{y^2}} \over {{{\sin }^2}\theta }}$ = 1 is greater than 2, then the length of its latus rectum lies in the interval :

Question

Let $0 < \theta < {\pi \over 2}$. If the eccentricity of the

hyperbola ${{{x^2}} \over {{{\cos }^2}\theta }} - {{{y^2}} \over {{{\sin }^2}\theta }}$ = 1 is greater

than 2, then the length of its latus rectum lies in the interval :

(3, $\infty $)

$\left( {{3 \over 2},2} \right]$

$\left( {1,{3 \over 2}} \right]$

$\left( {2,3} \right]$

Solution

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