Show that the straight lines `L_1=(b+c)x+a y+1=0,\ L_2=(c+a)x+b y+1=0\ n d\ L_3=(a+b)x+c y+1=0\ ` are concurrent.

Show that the straight lines L_(1)=(b+c)x+ay+1=0,L_(2)=(c+a)x+by+1=0ndL_(3)=(a+b)x+cy+1 are concurrent.

If a ,\ b ,\ c are in A.P. prove that the straight lines a x+2y+1=0,\ b x+3y+1=0\ a n d\ c x+4y+1=0 are concurrent.

To find the condition that the three straight lines A_(1)x+B_(1)y+C_(1)=0, A_(2)x+B_(2)y+C_(2)=0 and A_(3)x+B_(3)y+C_(3)=0 are concurrent.

Consider the lines give by L_1: x+3y -5=0, L_2:3x - ky-1=0, L_3: 5x +2y -12=0

If the lines a x+12 y+1=0,\ b x+13 y+1=0 and c x+14 y+1=0 are concurrent, then a , b , c are in

If the three lines a x+a^2y+1=0,\ b x+b^2y+1=0\ a n d\ c x+c^2y+1=0 are concurrent, show that at least two of three constants a , b ,\ c are equal.

L_(1)=x+3y-5=0,L_(2)=3x-ky-1=0,L_(3)=5x+2y-12=0 are concurrent if k=

Show that the straight lines x/a+y/b=1/c, x/b+y/c=1/a and x/c+y/a=1/b will be concurrent if ab+bc+ca=0

L_1=(a-b)x+(b-c)y+(c-a)=0L_2=(b-c)x+(c-a)y+(a-b)=0L_3=(c-a)x+(a-b)y+(b-c)=0 KAMPLE 6 Show that the following lines are concurrent L1 = (a-b) x + (b-c)y + (c-a) = 0 12 = (b-c)x + (c-a) y + (a-b) = 0 L3 = (c-a)x + (a-b) y + (b-c) = 0. ,

If the straight lines x+y-2=0,2x-y+1=0 and a x+b y-c=0 are concurrent, then the family of lines 2a x+3b y+c=0(a , b , c are nonzero) is concurrent at (a) (2,3) (b) (1/2,1/3) (c) (-1/6,-5/9) (d) (2/3,-7/5)