Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 4 - 4.3 - Conics - 4.3 Exercises - Page 339: 58


Length of the latera recta: $\frac{2b^2}{a}$

Work Step by Step

Use: $a^2=b^2+c^2$ $a^2-c^2=b^2$ Standard form when major axis is horizontal: $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ Let's find the values of $y$ when $x=±c$: $\frac{(±c)^2}{a^2}+\frac{y^2}{b^2}=1~~$ $\frac{y^2}{b^2}=1-\frac{c^2}{a^2}$ $\frac{y^2}{b^2}=\frac{a^2-c^2}{a^2}$ $\frac{y^2}{b^2}=\frac{b^2}{a^2}$ $y^2=\frac{b^4}{a^2}$ $y=±\frac{b^2}{a}$ One of the latera rectas, the one on the right side, goes from $(c,-\frac{b^2}{a})$ to $(c,\frac{b^2}{a})$. So, the length is: $\frac{b^2}{a}-(-\frac{b^2}{a})=\frac{2b^2}{a}$
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