Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - Summary Exercises on Graphs, Circles, Functions, and Equations - Exercises - Page 248: 23

Answer

$(4\pm\sqrt 7,2)$

Work Step by Step

Step 1. Given the circle with center at $(4,5)$ and radius $4$, we can write its equation as $(x-4)^2+(y-5)^2=16$ Step 2. To find the intersects, use $y=2$ in the equation above, we have $(x-4)^2+(2-5)^2=16\longrightarrow (x-4)^2=16-9=7$ which gives $x=4\pm\sqrt 7$ Step 3. The intersection points are $(4\pm\sqrt 7,2)$
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