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A diagonal of rhombus ABCD is a member o...

A diagonal of rhombus ABCD is a member of both the family of lines `(x + y +1) + lamda_1(2x+3y-2) = 0 and (x - y +2) + lamda_2(2x-3y+5)` where `lamda_1,lamda_2 in" R"` and one of the vertex of the rhombus is (3,2) . If area of the rhombus is `2sqrt5` square units then find the length of semi longer diagonal of the rhombus ..........

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A diagonal of rhombus ABCD is member of both the families of lines (x+y-1)+lambda(2x+3y-2)=0 and (x-y+2)+lambda(2x-3y+5)=0 and rhombus is (3,2). If the area of the rhombus is 12sqrt(5) sq.units,then find the remaining vertices of the rhombus.

If the two sides of rhombus are x+2y+2=0 and 2x+y-3=0, then find the slope of the longer diagonal.

Knowledge Check

  • Consider the family of lines (x+y-1)+lamda(2x+3y-5)=0 and (3x+2y-4)+mu(x_2y-6)=0 The equation of the straight line that belong to both the families is

    A
    `x-2y-8=0`
    B
    `x-2y+8=0`
    C
    `2x-y+8=0`
    D
    `2x-y+8=0`

  • The value of lamda , for which the lines 3x - 4y = 13, 8x - 11y = 33 and 2x - 3y + lamda = 0 are concurrent is

    A
    `-1`
    B
    `-7`
    C
    `1/7`
    D
    9

  • Equation of straight line belonging to families of straight lines (x+2y)+lamda(3x+2y+1)=0 and (x-2y)+mu(x-y+1)=0 is

    A
    6x+5y=2
    B
    5x-6y+4=0
    C
    5x+6y=4
    D
    None of the above

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    The area of the rhombus ABCD is 24. The equation of the diagonal BD is 4x + 3y + 2=0 and A (3,2) The length of the side of the rhombus is

    The equation of one of the diagonals of a rhombus is 3x + 4y - 7 = 0 . Find the equation of the other diagonal passing through (-1,-2) .

    The sides of a rhombus are parallel to y=2x+3 and 2y=x+5. The diagonals of the rhombus intersect at (1,2). If one vertex of the rhombus lies on the y-axis then possible values of the ordinates of this vertex are 1 (b) 2 (c) 3 (d) 4

    Consider the family of line (x+y-1)+lamda(2x+3y-5)=0 and (3x+2y-4)+mu(x+2y-6)=0 Equation of a straight line that belongs to both the families is:

    Locus of point of intersection of the perpendicular lines one belonging to (x + y -2) + lamda (2x+3y-5)=0 and other to (2x+y -11) + lamda(x+2y-13)=0 is a

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