If it is possible to draw a line which belongs to all the given family of lines `y-2x+1+lambda_(1)(2y-x-1)=0, 3y-x-6+lambda_(2)(y-3x+6)=0, ax+y-2+lambda_(3)(6x+ay-a)=0`, then

Distance possible to draw a line which belongs to all the given family of lines y-2x+1+lambda_1(2y-x-1)=0,3y-x-6+lambda_2(y-3x+6)=0,a x+y-2+lambda_3(6x+a y-a)=0 , then a=4 (b) a=3 a=-2 (d) a=2

The equation of straight line belonging to both the families of lines (x-y+1)+lambda_1(2x-y-2)=0 and (5x+3y-2)+lambda_2(3x-y-4)=0 where lambda_1, lambda_2 are arbitrary numbers is (A) 5x -2y -7=0 (B) 2x+ 5y - 7= 0 (C) 5x + 2y -7 =0 (D) 2x- 5y- 7= 0

If the equation of any two diagonals of a regular pentagon belongs to the family of lines (1+2lambda)y-(2+lambda)x+1-lambda=0 and their lengths are sin 36^0 , then the locus of the center of circle circumscribing the given pentagon (the triangles formed by these diagonals with the sides of pentagon have no side common) is (a) x^2+y^2-2x-2y+1+sin^2 72^0=0 (b) x^2+y^2-2x-2y+cos^2 72^0=0 (c) x^2+y^2-2x-2y+1+cos^2 72^0=0 (d) x^2+y^2-2x-2y+sin^2 72^0=0

A diagonal of rhombus A B C D is member of both the families of lines (x+y-1)+lambda1(2x+3y-2)=0 and (x-y+2)+lambda2(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.

The direction ratios of the line, given by the planes x - y + z - 5 = 0, x - 3y - 6 = 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.

If the lines 3x + 4y+ 1 = 0, 5x +lambda y + 3 = 0 and 2x + y-1 = 0 are concurrent, then lambda=

Find the locus of image of the veriable point (lambda^(2), 2 lambda) in the line mirror x-y+1=0, where lambda is a perimeter.

If line 3x-a y-1=0 is parallel to the line (a+2)x-y+3=0 then find the value of adot