The answer to the question never directly stated in the previous post is the following equation.
Where a varies from 0 to 1.
It’s an interesting equation, so I’m just going to consider it by itself, independent of the problem not really discussed.
Plotting that equation on the xy plane for various values of a (namely, 1/10 to 9/10 at increments of 1/10) produces the following picture.
Some nice symmetries going on there. But notice the way there seems to be a very definite boundary to the shape formed by all the ellipses overlayed. Is there a nice mathematical description of that shape?
Of course, there likely is, or I wouldn’t be talking about it.
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