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

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 (0,2) is (A) x-y-2=0 (B) x+y=0 (C) x-y=0 (D) 2x-y-3=0

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

Equation of the line belonging to the system 3x+2y-8+lambda(2x-5y+1)=0 and having equal intercepts is

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

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

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

The equation of the locus of the foot of perpendicular drawn from (5, 6) on the family of lines (x-2)+lambda(y-3)=0 (where lambda in R ) is