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Q)

The normal at the point $(bt_1^2, 2bt_1)$ on a parabola meets the parabola again in the point $(bt_2^2 , 2bt_2)$ then :


( A ) $t_2 = t_1 - \frac{2}{t_1}$
( B ) $t_2 = t_1 + \frac{2}{t_1}$
( C ) $t_2 = -t_1 + \frac{2}{t_1}$
( D ) $t_2 = -t_1 - \frac{2}{t_1}$

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A)
The equation of the normal at (bt1^2,2bt1) is y=-tx+2bt1+bt1^3 Sinse the normal passes through the point (bt2^2,2bt2) we have, 2bt2=-t1.bt2^2+2bt1+bt1^3 =>2b(t1-t2)=bt1t2^2-bt1^3=bt1(t2^2-t1^2) =>-2b(t2-t1)=bt1(t2-t1)(t2+t1) =>2=-t1(t2+t1)=>t2+t1=-2/t1 ==>t2=-t1-2/t1 So option D. is correct
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