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: 22


$x^2=8y$ Latus rectum points: $(-4,2),(4,2)$ See graph

Work Step by Step

We are given the parabola: Focus: $(0,2)$ Vertex: $(0,0)$ Because the vertex and the focus have the same $x$-coordinate, the parabola is vertical. Its standard equation is: $(x-h)^2=4p(y-k)$ Use the coordinates of the vertex to determine $h,k$: $(h,k)=(0,0)$ $h=0$ $k=0$ Determine $p$ using the coordinates of the focus: $(h,k+p)=(0,2)$ $(0,0+p)=(0,2)$ $p=2$ Determine the parabola's equation: $(x-0)^2=4(2)(y-0)$ $x^2=8y$ Determine the two points defining the latus rectum: $y=2$ $x^2=8(2)$ $x^2=16$ $x=\pm 4$ $\Rightarrow (-4,2),(4,2)$ Plot the points and graph the parabola:
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