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Q.
The locus of the middle points of the focal chords of parabola, $y^2=8 x$ is another parabola whose length of latus rectum is
Conic Sections
Solution:
$ 2 h = a \left( t _1^2+ t _2^2\right) \ldots(1)$
$ \text { and } 2 k =2 a \left( t _1+ t _2\right)$....(2)
$\text { and } t _1 t _2=-1 $
$ \text { from }(2) $
$ k ^2= a ^2\left[\frac{2 h }{ a }-2\right] $
$y ^2=2 a ( x -2 a ) $
$\text { Put a }=2$
$\text { Hence, } y ^2=4( x -4) $
