Question

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

a.  π/6

b. π/4

c. π/3

d. π/2

Answer 1

Correct option is c. π/3

Equation of tangent of the parabola y² = 4x is

y = mx + 1/m

This equation passes through (1, 4) i.e.

4 = m +1/m

m² – 4m+1 = 0

m₁ .m₂ = 1 and m₁ + m₂ = 4

Angle between the two tangents is tan θ = \(\begin{vmatrix}\frac{m_!-m_2}{1+m_1m_2}\end{vmatrix}\)

tanθ = \(\begin{vmatrix}\frac{\sqrt{(4)^2-4}}{1+1}\end{vmatrix}=\frac{\sqrt{12}}2=\sqrt{3}\)

∴θ = π/3