JEE Advanced 2009 Mathematics question

The tangent PT and the normal PN to the parabola at a point P on it meet its axis at points T and N, respectively. The locus of the centroid of the triangle PTN is a parabola whose

(A)vertex is Correct
(B)directrix is x = 0
(C)latus rectum is
(D)focus is (a, 0)Correct

Answer: (A),(D)

Solution

P = (at², 2at); the tangent meets the axis at T = (−at², 0) and the normal at N = (2a + at², 0). Centroid: , . Eliminating t: $ = (h -

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Question ID VK-037757