The angle between the tangents drawn from the point (1, 4) to the parabola y2=4x is [2004]

Question

The angle between the tangents drawn from the point (1, 4) to the parabola $y^{2} = 4 x$ is [2004]

Smart Achievers · Accepted Answer

(3)

If $m$ be the slope of the tangent to the parabola, then its equation is $y = m x + \frac{1}{m}$

Since the tangent passes through (1, 4)

$∴$ $4 = m + \frac{1}{m} \Rightarrow m^{2} - 4 m + 1 = 0$

If the angle between two tangents to the parabola be $θ$ , then

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

$= \frac{\sqrt{16 - 4}}{1 + 1} = \sqrt{3} \Rightarrow θ = \frac{π}{3}$

Want Us to Email you About Special Offers & Updates?