If the straight lines `a_(1)x+b_(1)y+c=0,a_(2)x+b_(2)y+c=0anda_(3)x+b_(3)y+c=0[cne0]` are concurrent , show that the points `(a_(1),b_(1),(a_(2),b_(2))and(a_(3),b_(3))` are collinear.

If the lines a_1x+b_1y+1=0,a_2x+b_2y+1=0 and a_3x+b_3y+1=0 are concurrent, show that the point (a_1, b_1),(a_1, b_2) and (a_3, b_3) are collinear.

The straight line a_(1)x+b_(1)y+c_(1)=0 anda_(2)x+b_(2)y+c_(2)=0 are parallel to each other if -

If the three straight lines ax + 2y + 1 = 0, 3y + bx + 1 = 0 and cx+ 4y + 1=0 are concurrent, then show that- a. b, c are in AP.

Show that two lines a_(1)x + b_(1) y+ c_(1) = 0 " and " a_(2)x + b_(2) y + c_(2) = 0 " where " b_(1) , b_(2) ne 0 are : (i) Parallel if a_(1)/b_(1) = a_(2)/b_(2) , and (ii) Perpendicular if a_(1) a_(2) + b_(1) b_(2) = 0 .

The lines ax + by + c = 0, where 3a + 2b + 4c= 0, are concurrent at the point (a) (1/2 ,3/4) (b) (1,3) (c) (3,1) (d) (3/4 ,1/2)

Statement - I: Equation of bisectors of the angles between the liens x=0 and y=0 are y=+-x Statement - II : Equation of the bisectors of the angles between the lines a_(1)x+b_(1)y+c_(1)=0anda_(2)x+b_(2)y+c_(2)=0 are (a_(1)x+b_(1)y+c_(1))/(sqrt(a_(1)^(2)+b_(1)^(2)))=+-(a_(2)x+b_(2)y+c_(2))/(sqrt(a_(2)^(2)+b_(2)^(2))) (Provided a_(1)b_(2)nea_(2)b_(1)andc_(1),c_(2)gt0)

If the lines x=a_(1)y+b_(1),z=c_(1)y+d_(1) and x=a_(2)y+b_(2),z=c_(2)y+d_(2) are perpendicular, prove that, 1+a_(1)a_(2)+c_(1)c_(2)=0 .

If the determinant of the matrix [(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))] is denoted by D, then the determinant of the matrix [(a_(1)+3b_(1)-4c_(1),b_(1),4c_(1)),(a_(2)+3b_(2)-4c_(2),b_(2),4c_(2)),(a_(3)+3b_(3)-4c_(3),b_(3),4c_(3))] will be -

If the simultaneous linear equations a_(1)x+b_(1)y+c_(1)=0 " and " a_(2)x+b_(2)y+c_(2)=0 have only one solution, then the required condition is -

If ab+bc+ca=0 then prove that the straight lines x/a+y/b=1/c,x/b+y/c=1/aand x/c+y/a=1/b are concurrent.