Question

If the lines x + (a – 1)y + 1 = 0 and 2x + a²y – 1 = 0 are     perpendicular then ……

(a) |a| = 2 

(b) 0 < a < 1

(c) – 1 < a < 1

(d) a = – 1

Answer 1

The correct option (d) a = – 1   

Explanation:

lines are perpendicular

∴ m₁ ∙ m₂ = – 1

slope of line x + (a – 1)y + 1 = 0 = m₁ = [(– 1)/(a – 1)]

slope of line 2x + a²y – 1 = 0 = m₂ = [(– 2)/(a²)]  

∴ [2/{a²(a – 1)}] = – 1

∴ 2 = a²(1 – a)

∴ a³ – a² + 2 = 0 

∴ (a + 1)(a² – 2a + 2) = 0

a² – 2a + 2 is not possible 

∴ a = – 1