Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 10 - Analytic Geometry - 10.2 The Parabola - 10.2 Assess Your Understanding - Page 647: 40


Vertex: $(0,0)$ Focus: $\left(2,0\right)$ Directrix: $x=-2$ See graph

Work Step by Step

We are given the parabola: $y^2=8x$ The standard equation is: $(y-k)^2=4p(x-h)$ Determine $h,k,p$: $h=0$ $k=0$ $4p=8\Rightarrow p=2$ Determine the vertex: $(h,k)=(0,0)$ Determine the focus: $(h+p,k)=\left(0+2,0\right)=\left(2,0\right)$ Determine the directrix: $x=h-p$ $x=0-2$ $x=-2$ Determine the two points defining the latus rectum: $x=2$ $y^2=4(2)(2)$ $y^2=16$ $y=\pm 4$ $\Rightarrow (2,-4),(2,4)$ Plot the points, draw the directrix, and graph the parabola:
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