Question
Maximum number of points on parabola $y^2 = 16x$ which are equidistant from a variable point $P$ (which lie inside the parabola), is -

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$1.$ The numbers $\left|A_1\right|,\left|A_2\right|, \ldots,\left|A_m\right|$ are distinct.
$2.$ $A_1, A_2, \ldots, A_m$ are pairwise disjoint.(Here $|A|$ donotes the number of elements in the set $A$ )Then, the maximum possible value of $m$ is