Mathematics

Problem

Two ellipses E1 and E2 share the same semi-minor axis length

b = 4

cm but have different semi-major axis lengths

a_1

and

a_2

with

a_1 < a_2

. Study the following. a. (i) Prove that the eccentricities

e_1

and

e_2

satisfy

e_1 < e_2

. b. (ii) Taking

a_1 = 5

cm and

a_2 = 6

cm, calculate

e_1

and

e_2

. c. (iii) Which ellipse is flatter? Justify your answer using both the numerical values and the inequality obtained in part (i).