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The equation 16 x^2-3y^2-3y^2-32 x+12 y-...

The equation `16 x^2-3y^2-3y^2-32 x+12 y-44=0` represents a hyperbola. the length of whose transvers axis is `4sqrt(3)` the length of whose transvers axis is `4` whose center is `(-1,2)` whose eccentricity is `sqrt((19)/3)`

A

length of the transverse axis is `2sqrt3`

B

length of each latus rectum is `32//sqrt(3)`

C

eccentricity is `sqrt(19//3)`

D

equation of a directrix is `x=(sqrt(19))/(3)`

Text Solution

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The correct Answer is:
A, B, C
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The equation 16x^(2)-3y^(2)-3y^(2)-32x+12y-44=0 represents a hyperbola.the length of whose transvers axis is 4sqrt(3) the length of whose transvers axis is 4sqrt(3) the length of whose transvers axis is 4 whose center is (-1,2) whose eccentricity is sqrt((19)/(3))

Find the eccentricity of the hyperbola,the length of whose conjugate axis is (3)/(4) of the length of transverse axis.

Knowledge Check

  • The equation 16x^(2)-3y^(2)-32x+12y-44=0 represents a hyperbola whose

    A
    transverse axis is `4sqrt3`
    B
    conjugate axis is 4
    C
    eccentricity is `(sqrt(19))/(sqrt(3))`.
    D
    centre is `(-1,2)`

  • The equation 16x^(2) - 3y^(2) - 32x + 12y - 44 = 0 represents a hyperbola

    A
    the length of whose transverse axis is `4sqrt(3)`
    B
    the length of whose conjugate axis is 4
    C
    whose centre is (-1,2)
    D
    whose eccentricity is `sqrt(19//3)`

  • The equation 16x^(2) - 3y^(2) - 32x - 12y - 44 = 0 represents a hyperbola, which one of the following is /are correct

    A
    the length of its transverse axis is `2 root () () 3 `
    B
    the length of its conjugate axis is 8
    C
    its centre is at `(1 , - 2)`
    D
    its eccentricity is `root () () 3`

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