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Q.
The locus of the mid point of the focal radii of a variable point $P$ moving on the parabola $y^2=8 x$, is a parabola whose latus rectum is
Conic Sections
Solution:
Clearly $2 h=a+a t^2$...(1)
and $2 k =2 at$ ....(2)
$\therefore$ On eliminating $t$ from(1)\&(2),
we get locus of $M(h, k)$ is
$y^2=4(x-1) \Rightarrow \text { Latus rectum }=4$
