Question

The angle between the tangents drawn from the point (1, 4) to the parabola y² = 4x is

(a) (π/2)

(b) (π/3)

(c) (π/4)

(d) (π/6)

Answer 1

The correct option (b) (π/3) 

Explanation:

Tangent to parabola having slope m is y = mx + (1/m)

This passes through (1, 4) ⇒ 4 = m + (1/m)

∴ m₂ – 4m + 1 = 0 ⇒ m₁m₂ = 1 and m₁ + m₂ = 4 ----- where m₁ & m₂ are the roots.

Now angle between line

tan θ  = |[(m₂ – m₁)/(1 + m₁m₂)]|

= |[√{(m₂ + m₁)² – 4m₁m₂}/(1 + m₁m₂)]| 

= |[√(16 – 4)/(1 + 1)]|

= |[√(12)/2]|

= √3 

∴  θ = tan^–1(√3) = (π/3).