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If the normal to \mathrm{y^2=4 x} at the point P meets the curve again at Q and \mathrm{y_1, y_2} are the ordinates of P and the midpoint of P Q respectively, then \mathrm{ \left|y_1 y_2\right|} is

Option: 1

5


Option: 2

3


Option: 3

4


Option: 4

2


Answers (1)

best_answer

\mathrm{\begin{aligned} & P \equiv\left(t^2, 2 t\right), Q \equiv\left(t_1^2, 2 t_1\right) \\ & y_1=2 t, y_2=t+t_1 \end{aligned}}

\mathrm{\begin{aligned} & y_1 y_2=2 t\left(t+t_1\right)=2 t\left(\frac{-2}{t}\right) \text { since } t_1=-t-\frac{2}{t} \\ & \therefore \quad\left|y_1 y_2\right|=4 . \end{aligned}}

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Nehul

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