Question

A normal chord of the parabola $y^2=4x$ subtending a right angle at the vertex makes an acute angle $\theta$ with the $x-$ axis the angle $\theta$ is equal to

• A. ${\cot }^{-1}\sqrt{2}$
• B. ${\tan }^{-1}\sqrt{3}$
• C. ${\sec }^{-1}\sqrt{3}$
• D. ${\tan }^{-1}\sqrt{2}$

Answer 1

The correct option is C ${\sec }^{-1}\sqrt{3}$

Let the normal be $y=mx–2m–m^3$
It subtending a right angle at the vertex then
$m=-\sqrt{2}\Rightarrow \theta =\sec -\sqrt{3}$