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The equation 3x^2+2hxy+3y^2=0 represents...

The equation `3x^2+2hxy+3y^2=0` represents a pair of straight lines passing through the origin . The two lines are

A

real and distinct if `h^2gt3`

B

real and distinct if `h^2gt9`

C

real and coincident if `h^2gt12`

D

real and coincident if `h^2gt3`

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A
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Knowledge Check

  • If the equation 2x^2-2hxy+2y^2=0 represents two coincident straight lines passing through the origin , then h is equal to

    A
    `+-6`
    B
    `sqrt(6)`
    C
    `-sqrt(6)`
    D
    `+-2`

  • The equation ax^(2)=2hxy+by^(2)=0 represented a pair of coincident lines through the origin if

    A
    `h^(2)=ab`
    B
    `2h=ab`
    C
    `a=bh`
    D
    `b=ah`

  • The equation x^(3)+x^(2)y-xy^(2)-y^(3)=0 represents three straight lines passing through the origin such that

    A
    two of them are coincident and two of them are perpendicular
    B
    two of them are coincident but not two are perpendicular
    C
    two of them are perpendicular but no two are coincident
    D
    none of these

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