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The equations of the transverse and conj...

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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The correct Answer is:
`rArr 10 8x^(2) - 312 xy - 17y^(2) + 744 x - 208 y - 520 = 0 `
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The equation of the transverse and conjugate axes of a hyperbola are respectively 3x+4y-7=0, 4x-3y+7=0 and their respective lengths are 4 and 6. Find the equation of the hyperbola.

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Knowledge Check

  • 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

    A
    ` (2)/(5) (x+2y -3)^(2) -(3)/(5) (2x-y+4)^(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 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`

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