(a)

Eccentricity of the sign call is .

Length of the sign is inch.

Elliptical track is in the form of horizontal ellipse.

Therefore,

The standard form of horizontal ellipse .

Eccentricity : .

Substitute and in above expression.

.

Consider . 

Substitute and in above expression.

.

. 

Therefore, maximum height of the sign is inch.

(b)

Find the equation for the ellipse If the origin is located at the center of the sign.

The ellipse equation with center at the origin is .

Substitute and  in above expression.

.

(a) The maximum height of the sign is inch.

(b) .