The edge of my kitchen counter top is the shape of an ellipse. Since my tiles were 18" squares, the deepest part is 18 inches deep and the edge tapers to 12 inches deep. The counter will be 6 feet long. You can see the counter outlined below if you look at the area that is both inside the blue ellipse and inside the brown rectangle at the same time.
What is the equation of this ellipse if everything is figured in inches?
Where do the foci of my “tacks” need to be placed to draw my counter edge?
How long should the “string” be to generate this curve?