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Find the relation between $'t_1'$ meets the parabola again at $'t_2'$ for the parabola $y^2=4ax$?

$\begin{array}{1 1}(a)\;t_1=-t_2-\large\frac{2}{t_2}\\(b)\;t_2=-t_1-\large\frac{2}{t_1}\\(c)\;2t_1=-3t_2-\large\frac{2}{t_2}\\(d)\;4t_1=-t_2-\large\frac{3}{t_2}\end{array}$

1 Answer

Parametric equation of normal at $(at_1^2,2at_1)$ is
Since it meet the parabola again at $(at_2^2,2at_2)$
$a(t_2-t_1)\neq 0$
$t_1$ and $t_2$ are different.
Hence (b) is the correct answer.
answered Feb 6, 2014 by sreemathi.v

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