So many lines!

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 $B$ .