If the lines `ax+by+c=0, bx+cy+a=0 and cx+ay+b=0 (a, b,c` being distinct) are concurrent, then
(A) `a+b+c=0`
(B) `a+b+c=1`
(C) `ab+bc+ca=1`
(D) `ab+bc+ca=0`

If the lines ax+y+1=0, x+by+1=0 and x+y+c=0 (a,b and c being distinct and different from 1) are concurrent the value of (a)/(a-1)+(b)/(b-1)+(c)/(c-1) is

If the lines a x+y+1=0,x+b y+1=0, and x+y+c=0(a , b , c being distinct and different from 1) are concurrent, then (1/(1-a))+(1/(1-b))+(1/(1-c)) is (a) 0 (b) 1 1/((a+b+c)) (d) none of these

If the lines x+a y+a=0,\ b x+y+b=0\ a n d\ c x+c y+1=0 are concurrent, then write the value of 2a b c-a b-b c-c adot

If the lines x+ay+a=0, bx+y+b=0, cx+cy+1=0 (a!=b!=c!=1) are concurrent then value of a/(a-1)+b/(b-1)+c/(c-1)=

If the equation x^(2 )+ 2x + 3 = 0 and ax^(2) +bx+c=0, a, b, c in R , have a common root, then a : b:c is

Prove that the lines ax+by + c = 0, bx+ cy + a = 0 and cx+ay+b=0 are concurrent if a+b+c = 0 or a+b omega + c omega^(2) + c omega = 0 where omega is a complex cube root of unity .

If the lines (a-b-c) x + 2ay + 2a = 0 , 2bx + ( b- c - a) y + 2b = 0 and (2c+1) x + 2cy + c - a - b = 0 are concurrent , then the prove that either a+b+ c = 0 or (a+b+c)^(2) + 2a = 0

If the system of equations ax + by + c = 0,bx + cy +a = 0, cx + ay + b = 0 has infinitely many solutions then the system of equations (b + c) x +(c + a)y + (a + b) z = 0 (c + a) x + (a+b) y + (b + c) z = 0 (a + b) x + (b + c) y +(c + a) z = 0 has

Supose directioncoisnes of two lines are given by u l+vm+wn=0 and al^2+bm^2+cn^2=0 where u,v,w,a,b,c are arbitrary constnts and l,m,n are directioncosines of the lines. For u=v=w=1 if lines are perpendicular then. (A) a+b+c=0 (B) ab+bc+ca=0 (C) ab+bc+ca=3abc (D) ab+bc+ca=abc

For a gt b gt c gt 0 , if the distance between (1,1) and the point of intersection of the line ax+by-c=0 and bx+ay+c=0 is less than 2sqrt2 then, (A) a+b-cgt0 (B) a-b+clt0 (C) a-b+cgt0 (D) a+b-clt0