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  4. Locus of the middle point of chords of parabola y2=4 x, tangents drawn at the ends of which intersect at right angle is a parabola whose

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Q. Locus of the middle point of chords of parabola $y^{2}=4 x$, tangents drawn at the ends of which intersect at right angle is a parabola whose

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Solution:

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To find locus of the middle point of all focal chords
$T = S _{1}$
$yk -2( x + h )= k ^{2}-4 h$ passes through $(1,0)$
$-2(1+h)=k^{2}-4 h$
Hence, locus is $y ^{2}=2 x -2=2( x -1)$.
Now, verify alternatives.