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Question:

If st = 1, then the tangent at P and the normal at S to the parabola meet at a point whose ordinate is

(t2+1)22t3

a(t2+1)2t3

a(t2+2)2t3

a(t2+1)22t3

Solution:

Tangent at P: ty = x + at^2 or y = x/t + at
Normal at S: y + xt = 2at + at^3
Solving, 2y = at + 2at + at^3
y = a(t^2 + 1) / 2t^3