Prove that the following sets of three lines are concurrent: `x/a=y/b=1, x/b+y/a=1\ a n d\ y=xdot`

Prove that the following sets of three lines are concurrent: (x)/(a)=(y)/(b)=1,(x)/(b)+(y)/(a)=1 and y=x

Prove that the following sets of three lines are concurrent: 15x-18y+1=0,12x+10y-3=0 and 6x+66y-11=0

Prove that the following lines are concurrent. (i)5x-3y=1 , 2x+3y=23 , 42x+21y=257 (ii) 2x+3y-4=0 , x-5y+7=0 , 6x-17y+24=0

Prove that the diagonals of the parallelogram formed by the lines x/a +y/b=1,x/b+y/a= 1, x/a + y/b = 2 and x/b + y/a = 2 are at right angles . Also find its area (a != b)

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. ,

Prove that the parallelogram formed by the straight lines : (x)/(a)+(y)/(b)=1 , (x)/(b)+(y)/(a)=1 , (x)/(a)+(y)/(b)=2 and (x)/(b)+(y)/(a)=2 is a rhombus.

Show that the following lines are concurrent: 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