A diagonal of rhombus `A B C D` 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.

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 ..........

The value of the lambda if the lines (2+3y+4)+lambda(6x-y+12)=0 are

Consider the family of lines 5x+3y-2+lambda_(1)(3x-y-4)=0 " and " x-y+1+lambda_(2)(2x-y-2)=0 . Find the equation of a straight line that belongs to both the families.

A member of the family of lines (x+y-1)+lambda(2x+3y-2)=0,lambda in R intersects a member of the family of lines (ax+y-2)+alpha(bx+4y-5)=0,alpha in R at a fixed point.The ordered pair (a,b) is

Consider the family of lines 5x+3y-2+lambda(3x-y-4)=0 and x-y+1+mu(2x-y-2)=0. The equation of a straight line that belonges to both the families is

The equation of line belonging to the family of lines (5x+3y-2)+lambda(3x-y-4)=0 , lambda in R ,and at greatest distance from (0,0) is

Consider the family of lines 5x+3y-2 + lambda (3x-y-4)=0 and x-y+1 + mu (2x - y - 2) = 0 Equation of straight line that belong to both families is ax+by-7=0 then a+b is

Locus of the image of the point (1,1) in the line (5x-2y-7)+lambda(2x-3y+6)=0 (lambda in R'), is

Locus of the image of the point (1,1) in the line (5x-2y-7)+lambda(2x-3y+6)=0lambda in R, is

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