Two tangents are drawn from a point $(-4, 3)$ to the parabola $y^2 = 16x$. If $\sigma$ is the angle between them, then the value of $\cos \sigma$ is
Step-by-Step Solution
Key Concept: Two tangents from an external point to a parabola have perpendicular slopes when the point lies on the directrix.
Given $P = (t^2, 2t)$ and $Q = \left(\frac{1}{t}, -\frac{7}{t}\right)$ lie on the directrix of $y^2 = 16x$. The directrix is $x = -4$. Since $(-4, 3)$ lies on the directrix of $y^2 = 16x$, the angle between tangents is $90°$. Therefore, $\cos 90° = 0$.
Correct Answer: 1