So many lines!

Geometry Level 5

A line \(M\) passing through a fixed point \(O\) intersects \(n\) given straight lines \(\{L_i \} \) at points \(\{B_i\}\) respectively. Suppose there is a point \(P\) on line \(M\) such that the following equation holds true

\[ \dfrac{n}{OP} = \sum_{i=1}^n \dfrac{1}{OB_i} \]

then what is the locus of all such points \(P\)?

Clarification: All the above points lie in \( {\mathbf{R}}^2 \) and \(AB\) denotes the minimum distance between the points \(A\) and \(B\).


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