Question

The Earth's orbit is an ellipse with the sun at one focus. The length of the major axi is 186,000,000 miles and the accentricity is 0.0167. Find the distance from the ends of the major axis to the sun. These are the greatest and least distances from the earth to the sun.

Answer 1

You have a = 93 (million miles)
e = c/a = 0.0167
so, c = 1.55
now just find a±c

Answer 2

a = 93,000,000 miles.
eccentricity = 0.0167
c/a = 167/10000
c = 167/10000 * 93,000,000 = 1,553,100
c^2 = a^2 - b^2
solve for b

make a sketch to see what calculations you need.