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The tangent PT and the normal PN to the parabola $$y^2 = 4ax$$ 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
vertex is $$\left(\frac{2a}{3}, 0\right)$$
directrix is x = 0
latus rectum is $$\frac{2a}{3}$$
focus is (a, 0)
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