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State the conditions under which the equ...

State the conditions under which the equation `lx^(2)+2mxy+2px+2qy+r=0` represents a pair of lines

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The correct Answer is:
`2pqm-lq^(2)-rm=0 & p^(2) ge rl`
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Knowledge Check

  • The condition that the equation ax^2+by^2+c(x+y)=0 to represents a pair of straight lines is

    A
    a+b=0 or c=0
    B
    `a+b=0 or c=0, ablt0`
    C
    `ab gt 0, c=0`
    D
    `a+bne0, cne0`

  • If the equation 9x^(2)+24xy+by^(2)-12x+2fy-12=0 represents a pair of parallel lines, the f=

    A
    `-4`
    B
    `-3`
    C
    `-8`
    D
    `-12`

  • Statement-I : If the equation 4x^(2)+mxy-3y^(2)=0 represents a pair of real and distinct lines then m in R . Statement-II : If the difference of the slopes of the lines kx^(2)-12xy + y^(2) = 0 is 2 then k is 30 Which of the above statement is correct :

    A
    only I
    B
    only II
    C
    Both I and II
    D
    Neither I nor II

    • Similar Questions

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    Find k, if the equation 2x^(2) + kxy - 6y^(2) + 3x + y + 1 = 0 represents a pair of lines. Find the point of intersection of the lines and angle between the lines for this value of k.

    If a and b positive numbers (altb) , then the range of values of k for which a real lambda be found such that equation ax^2+2lambdaxy+by^2+2k(x+y+1)=0 represent a pair of straight lines is

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