The normal drawn to the parabola y2 = 4ax at the point P(t1) meets the curve again at Q(t2) then

Condition is t 2 = - t 1 − 2 t 1 ⇒ t 1 2 + t 1 t 2 + 2 = 0 ⇒ Δ ≥ 0 ⇒ t 2 2 ≥ 8

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The normal drawn to the parabola y² = 4ax at the point P(t₁) meets the curve again at Q(t₂) then

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$t_{1} \leq - 2 \sqrt{2}$

$t_{2} \geq 2 \sqrt{2}$

$t_{1} \geq 2 \sqrt{2}$

$t_{2} \leq - 2 \sqrt{2}$

answer is B, D.

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Detailed Solution

Condition is $t_{2} = - t_{1} - \frac{2}{t_{1}}$
$\begin{array}{l} \Rightarrow t_{1}^{2} + t_{1} t_{2} + 2 = 0 \\ \Rightarrow Δ \geq 0 \Rightarrow t_{2}^{2} \geq 8 \end{array}$

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