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Directrix of Hyperbola

If t 1, t 2, ...

Question

If $t_{1}$ , $t_{2}$ , $t_{3}$ are three points on $y^{2} = 4 x$ such that normal at $t_{1}$ intersects the parabola at $t_{2}$ and normal at $t_{2}$ intersects the parabola at $t_{3}$ and $3 t_{1} + 13 t_{2} + 9 t_{3}$ then $t_{1}$

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-3

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-2

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Solution

The correct option is B 2
$t_{2} = - t_{1} - \frac{2}{t_{1}} a n d t_{3} = - t_{2} - \frac{2}{t_{2}} a n d 3 t_{1} + 13 t_{2} + 9 t_{3} = 0 \Rightarrow t_{1} = 2$

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