The function is .

(a).

Graph:

Graph of   where .

(b).

The height of the arc at its center .

The function is .

Substitue  in the above equation.

Observe the graph:

The height of the arc at its center is .

(c).

At what points the arc height is .

Substitue  in .

Since 

(d).

The function is .

Apply derivative on each side with respect to .

Substitute  in the above equation.

The slope is .

(a).

(b). .

(c). .

(d). The slope is .