The equation of an ellipse, whose center is at (0,0):

[(x^2)/(a^2)] +[(y^2)/(b^2)] = 1------------(i)

Also,

b^2 = a^2 -c^2-----------------------------(ii)

where

a = semi-major axis ----mean distance in this Problem.

b = semi-minor axis

c = focal distance, from the center

(x,y) is any point on the ellipse.

So,

perihelion +aphelion = 2a = 2(mean distance)

128.5 +aphelion = 2(142)

aphelion = 284 -128.5 = 155.5 million miles -------answer.

-----------------------------

Equation of Mars' orbit:

c = "a" minus perihelion = mean distance minus perihelion ----(1)

c = 142 -128.5 = 13.5 million miles

Hence,

b^2 = (142)^2 -(13.5)^2

b^2 = 19,981.75 --------------------------(***)

Therefore, the equation of Mars' orbit is

[(x^2)/(142^2)] +[(y^2)/(19,981.75)] = 1

[(x^2)/(20,164)] +[(y^2)/(19,981.75)] = 1-------------answer.