I have a plane in $R^3$ that is defined by:
$$ (E - O)/h \cdot (x - O) + h = 0 $$ $E$ is a point located on the plane. $O$ is the origin and h is the distance between $E$ and $O$. $x$ is a point where $P_n$ (below) intersects this plane.
If I have a set of $N$ unit vectors: $ \{P_n, n =1,2, \ldots, N\} $.
How do I calculate the plane equation so that $E$ is at a point that represents the center point of a circle whose circumference includes all the intersection points of the plane with $P_n$? Namely:
$$ \|P_1 - E\| = \|P_2 - E\| = \ldots = \|P_N-E\| $$
I need the computationally solve for $E$. Please recommend possible numerical methods I could use and how to implement them.