Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 11 - Section 11.1 - Parabolas - 11.1 Exercises: 3


F(p,0) x=-p (3,0) $x=-3$

Work Step by Step

$y^{2}=4px$ is the equation for a parabola opening horizontally. We can observe from the example equation $y^{2}=12x$ that the coefficient of y is 12 To find the p value set $12=4p$ (This will allow you to find the focus and directrix of a parabola centered at the origin) Now solve for p $3=p$ To find the focus use the focus coordinates (p,0) Substitute: The focus is at (3,0) To find the directrix use the directrix formula $x=-p$ Substitute: The directrix is $x=-3$ Keep in mind these formulas and coordinates are for finding the directrix and focus when the parabola's vertex is at (0,0).
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