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  4. If the point P(4 , - 2) is the one end of the focal chord PQ of the parabola y2=x , then the slope of the tangent at Q is

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Q. 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

NTA AbhyasNTA Abhyas 2022

Solution:

The equation of the tangent at $\left(4 , - 2\right)$ to
$y^{2}=x \, $ is $-2y=\frac{1}{2}\left(x + 4\right)$ Solution 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.