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: 25

Answer

$y^{2}=-8x$ The latus rectum has endpoints $(-2,-4)$ and $(-2,4)$
1563419766

Work Step by Step

1. The directrix is vertical$\quad \Rightarrow\quad $the axis of symmetry is horizontal. 2.$\quad $The focus lies on the line $y=0$. So does the vertex. 3.$\quad $The focus is left of the directrix, the parabola opens left. $a=2$ 4.$\quad $From Table 2, $\begin{array}{|c|c|c|c|} \hline {focus}&{directrix}&{equation}& ... opens\\ \hline {(h-a,k)}&{x=h+a}&{(y-k)^{2}=-4a(x-h)} &left \\ \hline \end{array}$ $(h-a,k)=(-2,0)\quad \Rightarrow$Vertex: $(0,0)$ The equation is $\quad (y-0)^{2}=-4(2)(x-0)$ that is, $\quad y^{2}=-8x$ 5. For $x=-2, \quad y^{2}=16\quad \Rightarrow\quad y=\pm 4$ The latus rectum (line segment parallel to the directrix, containing the focus) has endpoints $(-2,-4)$ and $(-2,4)$ We have enough details for the graph.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.