Question

If the points (a, 0), (0, b) and (1, 1) are collinear, then \(\frac 1a + \frac 1b\) =

(a) –1

(b) 1

(c) 0

(d) 2

Answer 1

Correct option is (b) 1

Given points are (a, 0), (0, b) and (1, 1)

x₁ ​= a, y₁ ​= 0, x_2​ = 0, y₂​ = b  and x − 3 = 1, y₃ ​= 1

Condition for collinearity

x₁​y₂​ + x₂​y₃​ + x₃​y₁ ​= x₂​y_1​ + x_3​y₂​ + x₁​y₃​ gives

ab + 0 + 0 = 0 + 1.b + a.1

⇒ ab = a + b

⇒ \(1 = \frac 1b + \frac 1a\)

⇒ \(\frac 1a + \frac 1b = 1\)