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The equation of the transverse and cojug...

The equation of the transverse and cojugate axes of a hyperbola are respectively `x+ 2y -3=0 ,2x -y+4=0`
and their respectively length are` sqrt 2 and 2//sqrt 3` . The equation of the hyperbola is

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The correct Answer is:
`(2x-y+4)^(2)-9(x+2y-3)^(2)=10`
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The equations of the transverse and conjugate axes of a hyperbola are respectively 3x + 4y - 7 = 0 , 4x - 3y + 8 = 0 and their respective lengths are 4 and 6. Find the equation of the hyperbola.

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Knowledge Check

  • The equations of transverse and conjugate axes of a hyperbola are respetively x+ 2y - 3 =0, 2x-y +4=0 and their respective length are sqrt2 and 2//sqrt3 . The equation of the hyperbola is

    A
    ` (2)/(5) (2x-y+4) ^(2) -(3)/(5) (x+2y-3) ^(2) = 1 `
    B
    ` (2)/(5) (2x- y+3)^(2) -(3)/(5) (x+2y -3)^(2) =1`
    C
    ` 2 ( 2x- y+4) ^(2) -3( x+2y-3) ^(2) =1`
    D
    ` 2(x+2y-3) ^(2) -3(2x- y +4) ^(2) =1`

  • The equation of the latusrectum of the hyperbola 3y^(2)-4x^(2)=12 are

    A
    `y=pm sqrt(11)`
    B
    `y=pm sqrt3`
    C
    `y=pm sqrt7`
    D
    `y=pm sqrt5`

  • The equations of the asymptotes of the hyperbola 4x^(2) -9y^(2) =36 are

    A
    `2x+-3y =0`
    B
    ` 2x+-5y =0`
    C
    ` 2x+-6y=0`
    D
    ` 2x+-8y=0`

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    One of the foci of the hyperbola is origin and the corresponding directrix is 3x + 4y + 1=0 .The eccentricity of the hyperbola is sqrt 5 .The equation of the hyperbola is

    The equation to the conjugate hyperbola of xy+ 3x- 4y +13=0 is

    A hyperbola passing through a focus of the ellipse x^(2)/(169)+y^(2)/(25)=1 . Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse. The product of eccentricities is 1. Then, the equation of the hyperbola is,

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