Precalculus (10th Edition)

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

Chapter 10 - Analytic Geometry - 10.4 The Hyperbola - 10.4 Assess Your Understanding - Page 669: 10

Answer

$(2,4)$ and $(2,-2)$.

Work Step by Step

If the transverse axis is parallel to the y-axis (as it can be seen on the figure), then the y-coordinates of the foci will be the same as the y-coordinate of the center. We can get the two foci's y-coordinates by adding and subtracting the given $a$-value from the centre's x-coordinate. Hence the 2 foci: $(2,1+a)=(2,1+3)=(2,4)$ and $(2,1-a)=(2,1−3)=(2,−2)$
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