Familiar figure

Geometry Level pending

A point \(P\) moves in such that the points \(A \bigg(\frac{1}{√2},\frac{-1}{√2}\bigg) \) and \(B \bigg(\frac{-1}{√2},\frac{1}{√2}\bigg) \) always subtend a right angle at \(P\).

Find the number of such points having integral coordinates.

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