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Prove that the bisectors of the between ...

Prove that the bisectors of the between the lines `ax^2+acxy+cy^2=0` and `(3+1/c)x^2+xy+(3+1/a)y^2=0` are always the same .

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The number of values of lambda for which the bisectors of the angle between the lines ax^(2)+2hxy+by^(2)+lambda(x^(2)+y^(2))=0 are the same as those of ax^(2)+2hxy+by^(2)=0 is

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Knowledge Check

  • The equation of the bisectors of angle between the lines x^(2)-4xy+y^(2)=0 is

    A
    `x^(2)+y^(2)=0`
    B
    `x^(2)-y^(2)=0`
    C
    `2x^(2)+y^(2)=0`
    D
    `x^(2)-2y^(2)=0`

  • If the bisectors of the angles between the lines given by 3x^(2)-4xy+5y^(2)=0 and 5x^(2)+4xy+3y^(2)=0 asre same, then, the angle made by the lines in the first pair with the second is

    A
    `30^(@)`
    B
    `60^(@)`
    C
    `45^(@)`
    D
    `90^(@)`

  • If the bisector of the angles between the lines in the two pairs 3x^(2)-4xy+5y^(2)=0 and 5x^(2)+4xy+3y^(2)-0 are same then the angle made by the first pair with the second is

    A
    `30^(@)`
    B
    `45^(@)`
    C
    `60^(@)`
    D
    `90^(@)`

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    The equation of the bisector of the obtuse angle between the lines x-y+2=0 , 7x+y+1=0 is

    The equation of the bisectors of the angle between the two straight lines 2x^(2)3xy+y^(2)=0 is

    If the bisectors of angles represented by ax^(2)+2hxy+by^(2)=0 and a'x^(2)+2h'xy+b'y^(2)=0 is same , then

    One of the bisector of the angle between the lines a(x-1)^2 + 2h(x-1)(y-2) + b (y-2)^2 = 0 is x + 2y - 5 = 0 . Then other bisector is (A) 2x-y=0 (B) 2x+y=0 (C) 2x+y-4=0 (D) x-2y+3=0

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