a.

A stone fireplace that was designed as an arch in the shape of a semi ellipse.

Height is at the center.

Width is feet along the base.

and .

Since it is in the form of

Foci is .

Therefore the thumbtacks are to be placed to the left and to the right at the center of the arch.

b.

The length of the string must be .

Reasoning :

With the string attached to the center of the foci of the arch and held tightly by small stick, the sum

of the distances from each thumbtack to the stick will remain constant.

When the stick is at one of the bottom corners of the arch, exactly from the center the distance from the far thumbtack and to the bottom corner will be :.

The distance from the other thumbtack and the bottom of the corner will be : .

Therefore the total length of the string needed is .

a.

The thumbtacks are to be placed to the left and to the right at the center of the arch.

b.

The length of the string must be .