Find the Dots

Math problems are Mohr fun when they involve circles.

Given 0 < tx < Rx and 0 < ty < Ry, two concentric but not necessarily similar ellipses are defined as x2/Rx2 + y2/Ry2 = 1 and x2/(Rx - tx)2 + y2/(Ry - ty)2 = 1.

Two circles, C1 and CN are defined as (x - Rx + tx/2)2 + y2 = (tx/2)2 and (y - Ry + ty/2)2 + x2 = (ty/2)2.

In between these circles are (N-2) circles denoted C2 through CN-1 with respective radii r2 through rN-1 whose edges are tangent to both ellipses and whose maximum overlap with each adjacent circle is given by m/2 × (rn + rn+1) where 0 ≤ m < 1, rn is the radius of one circle and rn+1 is the radius of the adjacent circle.

Find the number of circles N, the minimum possible constant value of the overlap ratio m, and the center coordinates and radii of all the circles.

Alternate problem: Instead of starting with C1 and CN defined as circles centered on the axes, C1 and CN are tangent to both ellipses and overlap the x and y axes, respectively, by mr1 and mrN, respectively.

Why do we care? By drawing every other circle, we can create a dotted CSS borders for curved corners. :)