If the normals at points $t_{1}$ and $t_{2}$ meet on the parabola then

t_{1} t_{2} = - 1

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t_{2} = - t_{1} - \frac{2}{t_{1}}

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t_{1} t_{2} = 2

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Solution

The correct option is C $t_{1} t_{2} = 2$
Normal at point $P (t_{1})$ meets the parabola again at point $R (t_{3})$ , then
$t_{3} = - t_{1} - \frac{2}{t_{1}}$
Also normal at point $Q (t_{2})$ meets the parabola at the same point $R (t_{3})$ , then
$t_{3} = - t_{2} - \frac{2}{t_{2}}$
Comparing these values of $t_{3}$ , we have
$- t_{1} - \frac{2}{t_{1}} = - t_{2} - \frac{2}{t_{2}}$
$\Rightarrow t_{1} t_{2} = 2$

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If the normals at points t1 and t2 meet on the parabola then

The correct option is C t1t2=2Normal at point P(t1) meets the parabola again at point R(t3), thent3=−t1−2t1Also normal at point Q(t2) meets the parabola at the same point R(t3), thent3=−t2−2t2Comparing these values of t3, we have−t1−2t1=−t2−2t2 ⇒t1t2=2

If the normals at points $t_{1}$ and $t_{2}$ meet on the parabola then