Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 11 - Section 11.2 - Ellipses - 11.2 Exercises - Page 797: 15

Answer

(a) Vertices: $V(0,±3)$ Foci: $F(0,±\sqrt 5)$ Eccentricity: $e=\frac{\sqrt 5}{3}$ (b) Length of the major axis: $2a=6$ Length of the minor axis: $2b=4$ (c)

Work Step by Step

$9x^2+4y^2=36$ $\frac{x^2}{4}+\frac{y^2}{9}=1$ $\frac{x^2}{2^2}+\frac{y^2}{3^2}=1$ The major axis is vertical. Equation of an ellipse when major axis is vertical (center at the origin): $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$ So: $a=3$ $b=2$ $c^2=a^2-b^2=3^2-2^2=9-4=5$ $c=\sqrt 5$ (a) Vertices: $V(0,±a)=V(0,±3)$ Foci: $F(0,±c)=F(0,±\sqrt 5)$ Eccentricity: $e=\frac{c}{a}=\frac{\sqrt 5}{3}$ (b) Length of the major axis: $2a=6$ Length of the minor axis: $2b=4$
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