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If a hyperbola passes through the focus of the ellipse `x^(2)/25+y^(2)/16=1` and its transverse and conjugate gate axis coincides with the major and minor axis of the ellipse, and product of their eccentricities is 1, then

A

equation of hyperbola `x^(2)/(9)-y^(2)/(16)=1`

B

equation of hyperbola `x^(2)/(9)-x^(2)/(25)=1`

C

focus of hyperbola (5, 0)

D

focus of hyperbola is `(5sqrt3,0)`

Text Solution

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The correct Answer is:
A,C
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If a hyperbola passes through foci of the ellipse x^2/5^2 + y^2/3^2 = 1 and its transverse and conjugate axes coincide with the major and minor axes of the ellipse and the product of their eccentricities is 1, then the product of length of semi transverse and conjugate axes of hyperbola is...

If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2)/(16)=1 . Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse and if the product of eccentricities of hyperbola and ellipse is 1 then the equation of a. hyperbola is (x^2)/9-(y^2)/(16)=1 b. the equation of hyperbola is (x^2)/9-(y^2)/(25)=1 c. focus of hyperbola is (5, 0) d. focus of hyperbola is (5sqrt(3),0)

Knowledge Check

  • Let a hyperbola passes through the focus of the ellipse (x^(2))/(25)+(y^(2))/(16)=1 . The transverse and conjugate axes of this hyperbola coincide with the major and minor axes of the given ellipse, also the product of eccentricities of given ellipse and hyperbola is 1, then

    A
    the equation of hyperbola is `(x^(2))/(9)-(y^(2))/(16)=1`
    B
    the equation of hyperbola is `(x^(2))/(9)-(y^(2))/(25)=1`
    C
    focus of hyperbola is `(5, 0)`
    D
    vertex of hyperbola is `(5sqrt(3), 0)`

  • Let a hyperbola has its transverse and conjugate axis coinciding with the major and minor axis of the ellipse (x^(2))/(25)+(y^(2))/(16)=1 respectively, if the hyperbola passes through one of the foci of the ellipse and the product of the eccentricities of hyperbola and ellipse is one, then

    A
    equation of hyperbola is `(x^(2))/(9)-(y^(2))/(16)=1`
    B
    focus of hyperbola is (5,0)
    C
    vertex of hyperbola is `(5sqrt(2),0)`
    D
    equation of hyperbola is `(x^(2))/(16)-(y^(2))/(25)=1`

  • The equation of the parabola whose vertex is at the centre of the ellipse x^2/25+y^2/16 = 1 and the focus coincide with the focus of the ellipse on the positive side of the major axis of the ellipse is

    A
    `y^2=3x`
    B
    `y^2=4x`
    C
    `y^2=5x`
    D
    `y^2=12x`

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