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: 2

Answer

F(0,p) y=-p (0,3) y=-3

Work Step by Step

$x^{2}=4py$ is the equation for a parabola opening vertically. We can observe from the example equation $x^{2}=12y$ 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 (0,p) Substitute: The focus is at (0,3) To find the directrix use the directrix formula $y=-p$ Substitute: The directrix is $y=-3$ Keep in mind these formulas and coordinates are for finding the the directrix and focus when the parabola's vertex is at (0,0).
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