The angle between the tangents drawn from the point (1, 4) to the parabola $y^{2} = 4 x$ is

\frac{π}{2}

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\frac{π}{3}

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\frac{π}{4}

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\frac{π}{6}

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Solution

The correct option is B $\frac{π}{3}$
Equation of tangent of slope m is $y = m x + \frac{1}{m}$ which passes through $(1, 4) \Rightarrow m^{2} - 4 m + 1 = 0$
$t a n θ = ∣ ∣ \frac{m_{1} - m_{2}}{1 + m_{1} m_{2}} ∣ ∣ \Rightarrow t a n θ = \frac{\sqrt{(m_{1} + m_{2})^{2}} - 4 m_{1} m_{2}}{1 + m_{1} m_{2}} \Rightarrow t a n θ = \frac{\sqrt{16 - 4}}{2} = \sqrt{3} ∴ θ = 60^{\circ}$

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