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If the lines given by ax^(2)+2hxy+by^(2)...

If the lines given by `ax^(2)+2hxy+by^(2)=0` are equally inclined to the lines given by `ax^(2)+2hxy+by^(2)+lambda(x^(2)+y^(2))=0`, then

A

`lambda` is any real number

B

`lambda=2`

C

`lambda=1`

D

none of these

Text Solution

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The correct Answer is:
A
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Show that pair of lines given by a^(2)x^(2)+2h(a+b)xy+b^(2)y^(2)=0 is equally inclined to the pair given by ax^(2)+2hxy+by^(2)=0

Show that the pair of lines given by a^2x^2+2h(a+b)xy+b^2y^2=0 is equally inclined to the pair given by ax^2+2hxy+by=0 .

Knowledge Check

  • If the line given by ax^(2)+2hxy+by^(2)=0 are equally inclined to the co-ordinate axes, then

    A
    `h=0`
    B
    `a+b=0`
    C
    `h^(2)-ab=0`
    D
    `h=a`

  • If two lines ax^(2)+2hxy+by^(2)=0 are equally inclined with co-ordinate axes, then

    A
    `h=0` and `ablt0`
    B
    `a=b`
    C
    `a=+-b`
    D
    `a^(2)+b^(2)=0`

  • The given between one of the lines give by ax^(2)+2hxy+by^(2)=0 and one of the lines ax^(2)+2hxy+by^(2)+lamda(x^(2)+y^(2))=0 is equal to the angle between the other two lines of the system then lamda =

    A
    2
    B
    3
    C
    4
    D
    any real number

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    If one of the lines given by ax^(2)+2hxy+by^(2)=0 is 4x-5y=0 then

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