Problem

Problem

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

\Delta PTN

is a parabola whose a. vertex is

\left(\frac{2a}{3}, 0\right)

b. directrix is at

x = 0

c. latusrectum is

\frac{2a}{3}

d. focus is

(a, 0)

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