Thank you for reporting, we will resolve it shortly
Q.
The locus of the mid point of the focal radii of a variable point moving on the parabola, $y^2=4 a x$ is a parabola whose
Conic Sections
Solution:
$ h =\frac{ a +\alpha}{2}, k =\frac{\beta}{2}$
$\Rightarrow \alpha=2 h - a , \beta=2 k$
$(\alpha, \beta)$ satisfies the parabola
$\therefore \beta^2=4 a \alpha $
$4 k ^2=4 a (2 h - a ) $
$ y ^2= a (2 x - a )$
$ y ^2=2 a \left( x -\frac{ a }{2}\right)$
