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

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Solution

The correct option is B

Equation of tangent of slope m is y = mx + $\frac{1}{m}$ which passes through (1,4) $\Rightarrow$ $m^{2}$ - 4m + 1 = 0

$tan θ = ∣ ∣ \frac{m_{1} - m_{2}}{1 + m_{1} m_{2}} ∣ ∣$ $\Rightarrow$ $tan θ = \frac{\sqrt{(m_{1} + m_{2})^{2} - 4 m_{1} m_{2}}}{1 + m_{1} m_{2}}$

$\Rightarrow$ $tan θ = \frac{\sqrt{16 - 4}}{2} = \sqrt{3}$

$∴$ $θ$ = $60^{\circ}$ .

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