Parabola 2 Question 17

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

(a) (t2+1)22t3

(b) a(t2+1)22t3

(c) a(t2+1)2t3

(d) a(t2+2)2t3

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Solution:

  1. PLAN Equation of tangent and normal at (at2,2at) are given by ty=x+at2 and y+tx=2at+at3, respectively.

Tangent at P:ty=x+at2 or y=xt+at

Normal at S:y+xt=2at+at3

Solving, 2y=at+2at+at3y=a(t2+1)22t3



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