On the graph, we will say the scale 1 unit = 1000 miles.

The equation of the ellipse might be , 
but we don't need that.

The center of the earth is at point C, one of the focal points of the
elliptical orbit of the satellite.  The red circle represents a cross section
of the earth.  We assume the radius of the earth is 4000 mile = 4 units.
The point S is the surface of the earth where the satellite is at its
highest distance above the surface of the earth.

We want to find the length of SA.

OB=b is the semi-minor axis and it is given as 12 units (12000 miles).

The Pythagorean relation for every ellipse is 

c²=a²-b²

We are given the eccentricity 0.6 = 

So c = OC = 0.6*OA = 0.6a, and we are given b = OB = 12 (12000 miles)

Substituting

















So OA = a = 15

and OC = c = 0.6a = .6(15) = 9 = 

SC = 4 (radius =4000 mi.)

OS = OC-SC = 9-4 = 5

So SA = OS+OA = 5+15 = 20

So the maximum altitude of the satellite is 20000 miles.

Edwin