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Parabola question

2009 · Shift 2 · Q35

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PYQ Library
JEE Advanced
Mathematics
Parabola
2009 · Shift 2 · Q35

Parabola question

2009 · Shift 2 · Q35

JEE AdvancedMathematicsParabolaMultiple correct+4 / −2

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

A
vertex is $\left( {{{2a} \over 3},0} \right)$
B
directrix is $x=0$
C
latus rectum is ${{{2a} \over 3}}$
D
focus is $(a, 0)$

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