Say I'm given an point P1 at coordinates $(x_1,y_1)$, and another point $P_2$ at coordinates $(x_2,y_2)$. Then I have a point $P_0$ that needs to be at coordinates $(x,y)$ such that it is a fixed distance $d_1$ from $P_1$ and a fixed distance $d_2$ from $P_2$. I understand then that I have two equations:
I'm not entirely sure how to go about finding $(x,y)$.
And then, how could I generalise the process, such that if I had $n$ points, $P_1$, $P_2, ..., P_n$, for which $P_0$ needed to be a given respective distance $d_1$, $d_2, ..., d_n $such that from each point, how would I go about finding $(x,y)$?
In particular, how could I do it such that every point cannot have an $x-$coordinate less than the x-coordinate of $P_1$?
And would it perhaps be better to think of this in terms of polar coordinates?
(For extra context, I'm trying to implement a python program that does this, but such that I start with two constraining points and equations, place the next point on the plane according to the constraints, which then becomes an additional constraint, and then take the next point and place it on the plane according to those constraints, and so on, until all the points have been placed.)