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If slope of one of the lines represented by `ax^(2)+2hxy+by^(2)=0 is n^(th)` power of the other then prove that `(ab^(n))^((1)/(n+1))+(a^(n)b)^((1)/(n+1))+2h=0`

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Knowledge Check

  • If the slope of one of the lines represented by ax^(2) + 2hxy + by^(2) = 0 is the square of the other, then (a+b)/h+(8h^(2))/(ab)

    A
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    C
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    D
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    A
    `(sqrt(3))/(2)`
    B
    `(1)/(2)`
    C
    `-(1)/(2)`
    D
    `-(3 sqrt(3))/(2)`

  • Statement-I : If two of the lines represented by ax^(3) + bx^(2)y + cxy^(2) + dy^(3) = 0 (a ne 0) make complementary angles with x-axis in anti-clockwise sense then slope of third line is a/d. Statement-II : If the slope of one of the line represented by ax^(2) + 2hxy + by^(2) = 0 is 'n' times the slope of another then ((1+n)^(2))/(n)=(h^(2))/(a b) Which of the above statement is correct :

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    Neither I nor II

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