The tangent \( P T \) and the normal \( P N \) to the parabola P \(...

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The tangent \( P T \) and the normal \( P N \) to the parabola
P \( y^{2}=4 a x \) at a point \( P \) on it meet its axis at points \( T \)

W. and \( N \), respectively. The locus of the centroid of the triangle \( P T N \) is a parabola whose:
(1) Vertex is \( \left(\frac{2 a}{3}, 0\right) \)
(2) Directrix is \( x=0 \)
(3) Latus rectum is \( \frac{2 a}{3} \)
(4) Focus is \( (a, 0) \)
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