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If eccentricity of the hyperbola (x^(2))...

If eccentricity of the hyperbola `(x^(2))/(cos^(2) theta)-(y^(2))/(sin^(2) theta)=1` is move than `2` when `theta in (0,(pi)/2)`. Find the possible values of length of latus rectum (a) `(3,oo)` (b) `1,3//2)` (c) `(2,3)` (d) `(-3,-2)`

A

(2,3)

B

`(3, oo)`

C

`(3//2, 2)`

D

`(1, 3//2)`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • If the eccentricity of the hyperbola (x^(2))/((1+sin theta)^(2))-(y^(2))/(cos^(2)theta)=1 is (2)/(sqrt3) , then the sum of all the possible values of theta is (where, theta in (0, pi) )

    A
    `(5pi)/(4)`
    B
    `(2pi)/(3)`
    C
    `(7pi)/(4)`
    D
    `pi`

  • Let 0 lt theta lt (pi)/2 . If the eccentricity of the hyperbola (x^(2))/(cos^(2)theta)-(y^(2))/(sin^(2)theta)=1 is greater ten 2, then the length of its latus rectum lies in the interval,

    A
    `(3,oo)`
    B
    `(3/2,2]`
    C
    `(1,3/2]`
    D
    `(2,3]`

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