Question

A straight line passes through a point A(1, 2) and makes an angle 60° with the x-axis. This line intersect the line x + y = 6 at P. Then AP will be

(a) 3(√3 + 1)

(b) 3(√3 – 1)

(c) (√3 + 1)

(d) 3√3

Answer 1

The correct option (b) 3(√3 – 1)   

Explanation:

x + y = 6 makes 45° with positive x axis. 

∴ ∠POX = 135°

Now in parametric form,

(x – 1)/(1/2)] = [(y – 2)/(√3/2)] = r

∴ x = (1/2)r + 1           and     y = (√3/2)r + 2

as        x + y = 6 ⇒ (r/2) + 1 + (√3/2)r + 2 = 6

∴ (√3 + 1)(r/2) = 3 ⇒ r = [6/(√3 + 1)]

∴ r = 3(√3 – 1)

i.e. AP = 3(√3 – 1)