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Let the eccentricity of the hyperbola (x...

Let the eccentricity of the hyperbola `(x ^(2))/(a ^(2))- (y ^(3))/(b ^(2)) =1` be reciprocal to that of the ellipse `x ^(2) + 9y ^(2) =9,` then the ratio `a ^(2) : b ^(2)` equals

A

`8:1`

B

`1:8`

C

`9:1`

D

`1:9`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • The eccentricity of the hyperbola 16x^(2)-9y^(2)=1 is?

    A
    `(3)/(5)`
    B
    `(5)/(3)`
    C
    `(4)/(5)`
    D
    `(5)/(4)`

  • The eccentricity of the hyperbola 9y^(2)-4x^(2)=36 is

    A
    `(5)/(2)`
    B
    `(sqrt(7))/(2)`
    C
    `(sqrt(13))/(2)`
    D
    2

  • Let the eccentricity of the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 be reciprocal to that of the ellipse x^(2) + 4y^(2) = 4 . If the hyperbola passes through a focus of the ellipse, then

    A
    the equation of the hyperbola is `x^(2)/3 - y^(2)/2 = 1`
    B
    a focus of the hyperbola is `(2, 0)`
    C
    the eccentricity of the hyperbola is `sqrt(5/3)`
    D
    the equation of the hyperbola is `x^(2) - 3y^(2) = 2`

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    Write the eccentricity of the hyperbola 9x^(2)-16y^(2)=144

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    Let the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 be reciprocal to that of the ellipse x^(2)+4y^(2)=4 . If the hyperbola passes through a focus of the ellipse then

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