Find the equation at normal to the parabola at point $P (a t^{2}, 2 a t)$ at $y^{2} = 4 a x$ .

y + t x = a t^{2} = 2 a t^{3}

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y + a t x = a t^{2} + 2 a t^{3}

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y + t x = a t^{3} + 2 a t

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Solution

The correct option is C $y + t x = a t^{3} + 2 a t$
$\begin{matrix} y^{2} = 4 a x 2 y \frac{d y}{d x} = 4 a \frac{d y}{d x} = \frac{2 a}{y} a t p (a t^{2}, 2 a t) \frac{d y}{d x} = \frac{2 a}{2 a t} S l o p e a t n o r m a l = - t S o, e q u a t i o n o f n o r m a l i s (y - 2 a t) = - t (x - a t^{2}) y + t x = a t^{3} + 2 a t . \end{matrix}$

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t

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