The locus of the middle points of parallel chords of a parabola $x^{2} = 4 a y$ is a

a straight line parallel to the

x -

axis

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a straight line parallel to the

y -

axis

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circle

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straight line parallel to a bisector of the angles between the axes

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Solution

The correct option is A a straight line parallel to the $y -$ axis
let $(h, k)$ be the middle point of parabola $x^{2} = 4 a y$
Then equation of chord is $T = S_{1}$
$\Rightarrow h x = 2 a (y + k)$
now, $s l o p e = \frac{h}{2 a} = λ (c o n s t a n t)$
Therefore, locus is $x = 2 a λ$
which is parallel to y axis

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