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Parametric Equation of Parabola

If a normal d...

Question

If a normal drawn to the parabola $y^{2} = 4 a x$ at the point $(a, 2 a)$ meets parabola again on $(a t^{2}, 2 a t)$ then the value of t will be?

1

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3

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Solution

The correct options are
A $1$
D $- 3$
$2 y \frac{d y}{d x} = 4 a$
$- \frac{d x}{d y} = - 1$
$(y - 2 a) = - (x - a)$
$- (y - 3 a) = x$ equation of the normal.
$y + x = 3 a$
$2 a t + a t^{2} = 3 a$
$t^{2} + 2 t - 3 = 0$
$(t + 1)^{2} = 4$
$t + 1 = \pm 2$
$t = 1, - 3$

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