Answer the following questions about the fundamental parameters of an ellipse centred…
MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices
Problem
Answer the following questions about the fundamental parameters of an ellipse centred at the origin and having its foci on the x-axis.
(i) State the definition of an ellipse in terms of a fixed constant sum of distances from two fixed points.
(ii) Let the foci be (±c,0) and the constant sum of distances be 2a. Explain logically why c<a must hold.
(iii) The semi-minor axis is denoted by b. Give a geometrical explanation of the relation b2=a2−c2 and describe what quantity b represents on the ellipse.