The centre of an ellipse is at the origin

MATHEMATICS · Multi-part · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

The centre of an ellipse is at the origin. Its vertices are at

(0,\,\pm6)

and its co-vertices are at

(\pm4,\,0)

. (i) Determine the lengths

a

and

b

and decide whether the major axis is vertical or horizontal. (ii) Write the standard equation of the ellipse. (iii) Calculate the value of

c

and give the coordinates of the foci.