Answer :

The equation of a parabola is y2 = 4ax, then,

On differentiating it with respect to x, we get


2y



Then, the slope of the tangent at (at2, 2at) is


Then, the equation of the tangent at (at2, 2at) is given by,


y – 2at =


ty -2at2 = x –at2


ty = x + at2


Now, Then, slope of normal at (at2, 2at)


=


Then, the equation of the normal at (at2, 2at) is given by:


y – 2at = -t(x-at2)


y – 2at = -tx + at3


y = -tx + 2at + at3


Therefore, the equation of the normal at (at2, 2at) is y = -tx + 2at + at3.


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