jee-advanced 2009 Q27

jee-advanced · India · paper2 Conic sections Locus and Trajectory Derivation

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

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

Paper Questions

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