If a normal drawn to the parabola y^2 = 4ax a | vedclass

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(D) The equation of the normal to the parabola $y^2 = 4ax$ at the point $t_1$ is $y = -t_1x + 2at_1 + at_1^3$.For the point $(a, 2a)$,we have $2a = t_

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$-3$

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(D) The equation of the normal to the parabola $y^2 = 4ax$ at the point $t_1$ is $y = -t_1x + 2at_1 + at_1^3$.For the point $(a, 2a)$,we have $2a = t_1(2a) \implies t_1^2 = 1$,so $t_1 = 1$ (since $y = 2a > 0$).The relation between the parameters of two points on the parabola where the normal at one point meets the parabola at another is given by $t_2 = -t_1 - \frac{2}{t_1}$.Substituting $t_1 = 1$ and $t_2 = t$:$t = -1 - \frac{2}{1} = -3$.

If a normal drawn to the parabola $y^2 = 4ax$ at the point $(a, 2a)$ meets the parabola again at $(at^2, 2at)$,then the value of $t$ is:

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