Question

The locus of the centroid of triangle $PSQ,$ where $PQ$ is any chord of the parabola $y^{2}=8\left(\right.x+2\left.\right)$ subtending right angle at the vertex and $S$ be its focus is also a parabola whose latus rectum is equal to

• A. $\frac{1}{3}$
• B. $\frac{4}{3}$
• C. $\frac{8}{3}$
• D. $2$

Answer 1

Answer: (C)

$t_{1}t_{2}=-4$
If $\left(h , k\right)$ is the centroid of $\Delta PSQ,$
Then $\frac{3 h + 4}{2}=t_{1}^{2}+t_{2}^{2},\frac{3 k}{4}=t_{1}+t_{2}$
$\Rightarrow k^{2}=\frac{8}{3}\left(\right.h-4\left.\right)$
$\therefore $ Latus rectum $=\frac{8}{3}$