Question

If the locus of the midpoint of contact of tangent drawn to the parabola $y^2=8x$ and foot of perpendicular drawn from its focus to the tangents is a conic then length of latus rectum of this conic is

• A. $\frac{9}{4}$
• B. $9$
• C. $18$
• D. $\frac{9}{2}$

Answer 1

The correct option is B $9$


Let the middle point of $P$ and $T$ be $(h,k)$. Then,
$2h=a{t}^2$
and $2k=3at$
$\therefore 2h=a.\frac{4k^2}{9a^2}$
The locus of $(h,k)$ is $2y^2=9ax$.
As $a=2$, we get
$y^2=9x$