College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 7 - Section 7.2 - The Parabola - 7.2 Assess Your Understanding - Page 515: 21

Answer

$y^{2}=16x$ The latus rectum has endpoints $(4,8)$ and $(4,-8)$
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Work Step by Step

Given: $a=4,\ (h,k)=(0,0)$ 1. The focus and the vertex lie on the horizontal line $\quad y=0.$ 2. The focus $(4,0)$ is right of the vertex $(0,0)$ So the parabola opens to the right. 3. By table 2, the equation is$\quad (y-k)^{2}=4a(x-h)$ that is, $\quad y^{2}=4(4)x,$ $y^{2}=16x$ 4. For $x=4, \quad y^{2}=64\Rightarrow y=\pm 8$ The latus rectum (line segment parallel to the axis, containing the focus) has endpoints $(4,8)$ and $(4,-8)$ 5. Directrix: $\quad x=h-a\quad \Rightarrow\quad x=-4$ We have enough details for the graph.
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