The three straight lines ax+by=c, bx+cy=a and cx +ay =b are collinear, if

Options

A. b+c=a
B. c+a=b
C. a+b+c=0
D. a+b=c

Answer

C

Explanation

Given lines are ` ax + by = x , bx + cy =a and cx + ay =b`
On adding the given three equations , we get
` ax + by + bx + cy + cx+ay = a + b + c`
` Rightarrow (a+b+c) x + (a+b+c) y = (a+b+c)`
On comparing with 0x + 0y = 0 for collinearity , we get a + b+c=0