MATH 264 Study Guide - Quiz Guide: Semi-Major And Semi-Minor Axes, Unit Circle, Ellipse

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 264
• Professor: Sancho

Document Summary

1. (a) we will try to nd a matrix a and a vector b such that the map v(cid:21) = a(cid:20)u. T (cid:20)u v(cid:21) + ~b sends (0, 0) to the center of the ellipse, and the points (1, 0) and (0, 1) to the endpoints of the semimajor and semiminor axes, respectively. We could have chosen other points on the circle, but these simplify the computation. The center of the ellipse is the intersection of the lines y = . 2 x 5 endpoints of the semimajor and semiminor axes, so let us rewrite the two lines as. We next want to locate the which is the point (6, 4), so ~b is the vector (cid:20)6. 4(cid:21) =(cid:20)2 y(cid:21) (cid:20)6 (cid:20)x y(cid:21) (cid:20)6 (cid:20)x where s and t are parameters. We can now nd the endpoints of the axes: = 13 t = 1, y(cid:21) =(cid:20) 6 (cid:20)x y(cid:21) =(cid:20)2 (cid:20)x.