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If ax^2+2hxy+by^2+2gx+2fy+c=0 represents...

If `ax^2+2hxy+by^2+2gx+2fy+c=0` represents a pair of lines then prove that
`triangle=abc+2fgh-af^2-bg^2-ch^2=0`.

Answer

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If ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of lines then prove that h^2geab,f^2gebc,g^2geac .

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Knowledge Check

  • If ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of parallel lines then sqrt([q^2-ac/f^2-bc])=

    A
    `a/b`
    B
    `sqrt([a/b])`
    C
    `sqrt([b/a])`
    D
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  • If ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents a pair of parallel lines then sqrt((g^(2)-ac)/(f^(2)-bc))=

    A
    `(a)/(b)`
    B
    `sqrt((a)/(b))`
    C
    `sqrt((b)/(a))`
    D
    `(b)/(a)`

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