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

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 , a x+y-2+lambda_3(6x+a y-a)=0 , then (a) a=4 (b) a=3 (c) 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

The straight line x+y+1+ lambda (2x-y-1)=0 is bot to 2x+3y-8=0, find the value of lambda .

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

Find the real values of lambda for which the following system of linear equations has non -trivial solutions: x+y-3z=0,( 1+lambda)x+(2+lambda)y-8z=0 , x-(1+lambda)y+(2+lambda)z=0 .

The line y=x+lambda is tangent to the ellips 2x^2+3y^2=1 Then lambda is

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 a circle passes through the points of intersection of the coordinates axes with the lines lambdax-y+1=0 and x-2y+3=0 , then find the value of lambda .

Find the obtuse angle between the lines x-y+2=0 and (2-sqrt(3))x-y+1=0 .

Find equation of the line which is equidistant from parallel lines 9x+6y-7=0 and 3x+2y+6= 0 .