A geometry problem by Pankhuri Agarwal

Geometry Level pending

Consider a circle in the \(XY\) plane with diameter \(1\), passing through the origin \(O\) and through a point \(A=(1,0)\). For any point \(B\) on the circle, let \(C\) be the point of intersection of the line \(OB\) with the vertical line through \(A\). If \(M\) is the point on the line \(OBC\) such that \(OM\) and \(BC\) are of equal length, then the locus of point \(M\) as \(B\) varies is given by the equation \(\text{__________} \).

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