A fireplace is to be constructed in the shape of a semi-ellipse (half of the ellipse). The opening is to have a height of 2 feet at the center and a width of 5 feet along the base. The contractor who has been hired to construct the fireplace wants to draw an outline of the shape on the wall using thumb tacks and a string. Where should the tacks be placed and what should be the length of the string?
I believe I need to use arc length for the string length, but I don't know how to go about it exactly.
Using for example the Wiki article on ellipses, you will find that the semi-major axis is $2.5$ feet and the semi-minor axis is $2$ feet. This means the foci are at $\pm 1.5$ feet, i.e.the tacks should be placed at the base, $1.5$ feet to either side of the center. The string should be $5$ feet long.