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If the equation `ax^(2)+2hxy+by^(2)+2gx+2fy+c=0` represents a pair of parallel lines, then

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If the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 resents a pair of parallel lines then prove that

If the equation ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of parallel lines, prove that h=sqrt(ab) and gsqrt(b)=fsqrt(a)or (h=-sqrt(ab)and gsqrt(b)=-fsqrt(a)) . The distance between them is 2sqrt((((g^2-ac))/(a(a+b)))) .

Knowledge Check

  • If the equation ax^(2)+hxy+by^(2)+4gx+6fy+4c=0 represents a pair of lines then

    A
    `4abc+4fgh=4.5af^(2)+4bg^(2)+h^(2)`
    B
    `4abc+6fgh-9af^(2)-4bg^(2)-ch^(2)`
    C
    `4abc+2fgh-9af^(2)+2bg^(2)+h^(2)`
    D
    `4abc+12fgh-9af^(2)+4bg^(2)+2h^(2)`

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