The ellipse equation is .

(a) Graph the model of the cam.

Graph :

Graph the equation .

(b) The ellipse equation is .

Here and and and .

The foci of a horizontally oriented ellipse are given by .

.

Substitute and and in .

Foci is .

The right focus is located at  ,so the graph of needs to be shifted  units to the left for the focus to be at the origin.

Therefore, the translated equation is .

(c) Find the equation of the model in part ,when the cam is rotated to an upright position.

For the cam to be rotated to an upright position ,it needs to be rotated counterclockwise through an angle of .

The rotation equations are and .

Substitute .

in .

.

Substitute in .

.

Substitute and in .

.

Therefore, the equation of the model in part ,when the cam is rotated to an upright position is given by .

(a) Graph :

Graph of the equation is

(b) The translated equation is .

(c)  .