Q. The chord PQ of the parabola $y^2 = x$, where one end P of the chord is at point (4, - 2), is perpendicular to the axis of the parabola. Then the slope of the normal at Q is
AIEEEAIEEE 2012Conic Sections
Solution:
Point P is $(4, -2)$ and PQ $\bot$ x-axis
So, $Q = (4, 2)$
Equation of tangent at $(4, 2)$ is
$yy_{1} = \frac{1}{2}\left(x+x_{1}\right)$
$\Rightarrow 2y = \frac{1}{2} \left(x+2\right) \Rightarrow 4y = x+2$
$\Rightarrow y = \frac{x}{4} + \frac{1}{2}$
So, slope of tangent $= \frac{1}{4}$
$\therefore $ Slope of normal $= - 4$
