Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 10 - Section 10.5 - Conic Sections - 10.5 Exercises - Page 708: 3

Answer

Vertex: $(0,0)$ Focus: $\left(-\frac{5}{12},0\right)$ Directrix: $x=\frac{5}{12}$

Work Step by Step

Recall: The parabola $y^2=4px$ has a vertex $(0,0)$, a focus $(p,0)$ and a directrix $x=-p$. We have $5x+3y^2=0$ or equivalently $y^2=\frac{-5x}{3}$. Then, $4p=-\frac{5}{3}$ $p=-\frac{\frac{5}{3}}{4}$ $p=-\frac{5}{12}$ So, the vertex is $(0,0)$, the focus is $(-\frac{5}{12},0)$, and the directris is $x=\frac{5}{12}$. Sketch the graph:
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