Show that the following lines are concurrent: `L_1=(a-b)x+(b-c)y+(c-a)=0` `L_2=(b-c)x+(c-a)y+(a-b)=0` `L_3=(c-a)x+(a-b)y+(b-c)=0`

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.

Prove that the lines (b-c)x+(c-a)y+(a-b)=0, (c-a)x+(a-b)y+(b-c)=0 and (a-b)x+(b-c)y+(c-a)=0 are concurrent.

The equation of the plane through the intersection of the plane a x+b y+c z+d=0\ a n d\ l x+m y+n+p=0 and parallel to the line y=0,\ z=0. (A) (b l-a m)y+(c l-a n)z+d l-a p=0 (B) (a m-b l)x+(m c-b n)z+m d-b p=0 (c) (n a-c l)d+(b n-c m)y+n d-c p=0 (D) None of these

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)

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)

If 4a^2+b^2+2c^2+4a b-6a c-3b c=0, then the family of lines a x+b y+c=0 may be concurrent at point(s) (-1,-1/2) (b) (-1,-1) (-2,-1) (d) (-1,2)

If a b+b c+c a=0, then solve a(b-2c)x^2+b(c-2a)x+c(a-2b)=0.

Show that the reflection of the line a x+b y+c=0 on the line x+y+1=0 is the line b+a y+(a+b-c)=0 where a!=bdot

Show that the reflection of the line a x+b y+c=0 on the line x+y+1=0 is the line bx+a y+(a+b-c)=0 where a!=bdot

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