First slide

Parabola

Question

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

Moderate

A

$\frac{π}{6}$
B

$\frac{π}{4}$
C

$\frac{π}{3}$
D

$\frac{π}{2}$

Solution

$y = m x + \frac{1}{m}$
The above tangent passes through (1, 4). So,
$\begin{array}{l} 4 = m + \frac{1}{m} \\ or m^{2} - 4 m + 1 = 0 \end{array}$
Now, angle between the lines is given by
$\tan θ = |\frac{m_{1} - m_{2}}{1 + m_{1} m_{2}}| \begin{matrix} = \frac{\sqrt{{(m_{1} + m_{2})}^{2} - 4 m_{1}} m_{2}}{1 + m_{1} m_{2}} \\ = \frac{\sqrt{16 - 4}}{1 + 1} = \sqrt{3} \end{matrix}$
$or θ = \frac{π}{3}$

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