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If the distance between the foci and the distance between the two directricies of the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` are in the ratio 3:2, then `b : a` is `1:sqrt(2)` (b) `sqrt(3):sqrt(2)` `1:2` (d) `2:1`

A

`1:sqrt2`

B

`sqrt3:sqrt2`

C

`1:2`

D

`2:1`

Text Solution

Verified by Experts

The correct Answer is:
A
Given that
`("Distance between foci")/("Distance between two directrices")=(3)/(2)`
`"or "(2ae)/(2*a//e)=(3)/(2)`
`"or "e^(2)=(3)/(3)`
`"or "1+(b^(2))/(a^(2))=(3)/(2)`
`"or "(b)/(a)=(1)/(sqrt2)`
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If the distance between the foci and the distance between the two directricies of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 are in the ratio 3:2, then b : a is (a) 1:sqrt(2) (b) sqrt(3):sqrt(2) (c) 1:2 (d) 2:1

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Knowledge Check

  • The distance between the foci of a hyperbola is 16 and e = sqrt2 . Its equation is

    A
    `x^(2) -y^(2) = 32`
    B
    `y^(2) -x^(2) = 32`
    C
    `x^(2) - y^(2) = 16`
    D
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  • Equation of a hyperbola such that the distance between the foci is 16 and eccentricity is sqrt(2) is

    A
    `x^2 - y^2 = 16`
    B
    `x^2 - y^2 = 32`
    C
    `x^2 - 2y^2 = 16`
    D
    `2x^2 - y^2 = 27`

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