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  4. If the locus of middle point of point of contact of tangent drawn to the parabola y2=8 x and the foot of perpendicular drawn from its focus to the tangent is a conic then find the length of latus rectum of the conic.

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Q. If the locus of middle point of point of contact of tangent drawn to the parabola $y^2=8 x$ and the foot of perpendicular drawn from its focus to the tangent is a conic then find the length of latus rectum of the conic.

JEE AdvancedJEE Advanced 2018

Solution:

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$( h , k )$ is mid point of PT then
$\Rightarrow 2 h = a \cdot \frac{4 k ^2}{9 a ^2} $
$\Rightarrow 2 y ^2=9 ax $
$a =2 $
$y^2=9 x $
$\text { L.R }=9 $