Ellipse has its foci at and a vertex at

MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Ellipse

S_1

has its foci at

(\pm 3, 0)

and a vertex at

(5, 0)

. Ellipse

S_2

has its foci at

(\pm 4, 0)

and is known to have the same eccentricity as

S_1

. Solve the following. (i) For

S_1

, calculate the lengths of the semi-major axis and semi-minor axis, and determine its eccentricity. (ii) For

S_2

, determine the length of its semi-major axis. (iii) For

S_2

, find the length of its latus rectum and state whether it is longer or shorter than that of

S_1