Mathematics

Problem

An ellipse has its centre at the origin and foci at

(\pm4,0)

. For every point

P

on the curve,

PF_{1}+PF_{2}=12

, where

F_{1}

and

F_{2}

denote the two foci. a. (i) Find the values of

a

and

c

for this ellipse. b. (ii) Determine

b

and hence derive the Cartesian equation of the ellipse in standard form. c. (iii) Calculate the eccentricity of the ellipse.