Parabola Ques 9

  1. If chord $P Q$ subtends an angle $\theta$ at the vertex of $y^2=4 a x$, then $\tan \theta$ is equal to

(a) $\frac{2}{3} \sqrt{7}$

(b) $\frac{-2}{3} \sqrt{7}$

(c) $\frac{2}{3} \sqrt{5}$

(d) $\frac{-2}{3} \sqrt{5}$

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Answer:

Correct Answer: 9.(d)

Solution: (d) $m_{O P}=\frac{2 a t-0}{a t^2-0}=\frac{2}{t}$

$ m_{O Q}=\frac{-2 \alpha / t}{a t^2}=-2 t $

$\therefore \quad \tan \theta=\frac{\frac{2}{t}+2 t}{1-\frac{2}{t} \cdot 2 t}=\frac{2\left(t+\frac{1}{t}\right)}{1-4}=\frac{-2 \sqrt{5}}{3}$

where $\quad t+\frac{1}{t}=\sqrt{5}$



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