Q.Find the equation of the normal to the parabola $y^2=4ax$ at the point $(at^2,\,2at)$.

Find the tangent's slope by implicit differentiation of $y^2=4ax$, evaluate it at $(at^2,2at)$, take the negative reciprocal for the normal's slope, then write the point-slope line.

Differentiating $y^2=4ax$: $2y\,y'=4a\Rightarrow y'=\dfrac{2a}{y}$

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