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.

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.

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.

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

Prove that : |{:(0,a-b,a-c),(b-a,0,b-c),(c-a,c-b,0):}|=0

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.

The area of a parallelogram formed by the lines a x+-b y+-c=0 is (a) (c^2)/((a b)) (b) (2c^2)/((a b)) (c) (c^2)/(2a b) (d) none of these

If a, b, c are rational and no two of them are equal, then the equations (b-c)x^(2)+(c-a)x+(a-b)=0 and, a(b-c)x^(2)+ b(c-a)x+c(a-b)=0

The equation (b-c)x+(c-a)y+(a-b)=0 and (b^3-c^3)x+(c^3-a^3)y+a^3-b^3=0 will represent the same line if

If a+b+c=0 and a,b,c are rational. Prove that the roots of the equation (b+c-a)x^(2)+(c+a-b)x+(a+b-c)=0 are rational.