Question

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

Options

• b + c = a

• c + a = b

• a + b + c = 0

• a + b = c

Answer 1

The three straight lines ax + by = c, bx + cy = a and cx + ay = b are collinear, if a + b + c = 0.

Explanation:

Given lines are ax + by = c, bx + cy = a and cx + ay = b 

On adding the given three equations, we get

ax + by + bx + cy + cx + ay = a + b + c

`\implies` (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