ParabolaHard

Question

The tangent PT and the normal PN to the parabola y2 = 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

Options

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

Solution

       
G ≡ (h, k)
⇒ h = , k =
⇒
⇒ required parabola is

⇒ y2 =
Vertex ≡ ; Focus ≡ (a, 0)

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