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Find the value of h if the slopes of the...

Find the value of h if the slopes of the lines represented by `6x^(2)+2hxy+y^(2)=0` are in the ratio 1:2.

Text Solution

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The correct Answer is:
`+-(3sqrt(3))/(2)`
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Knowledge Check

  • If the slopes of the lines represented by 6x^(2)+2hxy+y^(2)=0 are in the ratio 1:2 then h=

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

  • Assertion (A) : The slopes of one line represented by 2x^(2)–5xy+2y^(2) = 0 is 4 times the slope of the second line. Reason (R): If the slopes of lines represented by ax^(2)+2hxy+by^(2)=0 are in m:n then ((m+n)^(2))/(mn)=(4h^(2))/(ab)

    A
    A is true, R is true and R `rArr A`
    B
    A is true, R is true and `R cancel rArr A`
    C
    A is true, R is false
    D
    A is false, R is true

  • 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
    4
    B
    5
    C
    6
    D
    8

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    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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