Hey!
The equation of normal/perpendicular line to the parabola to the parabola (y^2 = 4ax) at the point (at^2,2at) is given by
y = at^3+2at−tx. (at the above mentioned points).
The above given equation is in parametric form of parabola (generalized form).
Hope it helped to clear your delimma.
Thank you.
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