Question

If the point $P\left(4,-2\right)$ is the one end of the focal chord $PQ$ of the parabola $y^2=x$ , then the slope of the tangent at $Q$ is

• A. $-1/4$
• B. $1/4$
• C. $4$
• D. $-4$

Answer 1

Answer: (C)

The equation of the tangent at $\left(4,-2\right)$ to
$y^2=x$ is $-2y=\frac{1}{2}\left(x+4\right)$ or $x+4y+4=0$
Its slope is $-1/4$
Therefore the slope of the perpendicular line is $4$ . Since the tangents at the end of focal chord of a parabola are at right angle, the slope of the tangent at $Q$ is $4$ . Hence (C) is the correct answer.