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The tangent PT and the normal PN to the parabola $y^{2} = 4 a x$ at a point P on it meet its axis at points T and N, respectively. The locus of the Centriod of the triangle PTN is a parabola whose

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vertex is $(\frac{2 a}{3}, 0)$

directrix is x = 0

latus rectum is $\frac{2 a}{3}$

focus is (a, 0)

answer is A, D.

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Detailed Solution

$3 h = 2 a + a t^{2} 3 k = 2 a t 3 h = 2 a + \frac{a .9 k^{2}}{4 a^{2}} y^{2} = \frac{4 a}{9} (3 x - 2 a) y^{2} = \frac{4 a}{3} (x - \frac{2 a}{3})$

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