Distance between ellipses with horizontal and vertical axes

      Example.

The distance between  x=cos(t)+1, y=1.5*sin(t)+2  and  x=2*cos(t)+5, y=sin(t)+4

With N=6 and CLICK:  d = 1.5157352350416644   1.515735
If I try again:  d = 1.5157369316041123   1.515737
The algorithm takes 2*107 points of the two ellipses at random. If I repeat I get slightly different values.
I can take 1.515735±0.000005
Similarly the closest points are (1.760±0.001,2.974±0.002) and (3.077±0.001,3.725±0.001)

The ellipses with WolfranAlpha:

parametric (cos(t)+1, 1.5*sin(t)+2), parametric (2*cos(t)+5, sin(t)+4)

If I want more precise values taking longer I can do:
with N=7 and click+:  d = 1.5157353097279447   1.5157353
and:   d = 1.5157353055879226   1.5157353
I can take d = 1.5157353±0.0000001
With N=8 and click++  I obtain d = 1.51573524±0.00000001

I one ellipse is a point ...
The distance from (10, 10) and the curve x=2*cos(t)+2, y=5*sin(t)-1

distance = 9.644700186961     nearest point of the curve = (2.815579, 3.565380)

With WolfranAlpha:

parametric (2*cos(t)+2, 5*sin(t)-2), parametric (0.2*cos(t)+10, 0.2*sin(t)+10)