The tangent and the normal to the parabola at a point on it meet its axis at points and

MATHEMATICS · Multi correct · CBSE · Mathematics · Conic Sections · Conic Sections

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

\triangle PTN

is a parabola whose (1) vertex is

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

(2) directrix is

x=0

(3) latus rectum is

\frac{2a}{3}

(4) focus is

(a,0)