Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 9 - Section 9.3 - The Parabola - Exercise Set - Page 997: 30



Work Step by Step

General form of a horizontal parabola is given as: $(y-k)^2=4p(x-h)$...(1) Here, $\text{Vertex}=(h,k)$ and focus is: $(h+p, k)$ General form of a vertical parabola is given as: $(x-h)^2=4p(y-k)$...(2) Here, $\text{Vertex}=(h,k)$ and focus is: $(h, k+p)$ As we are given focus: $(7,-1)$ Thus, from both forms of a parabola , we have two equations$k-p=-9$ and $k+p=-1$ Add these two equations, we get: $k=-5$ Thus, $p=-1-k=-1-(-5)=4$ From equation (1), we have $(x-7)^2=4(4)(y-(-5))$ or, $(x-7)^2=16(y+5)$ or, $y=\dfrac{1}{16}(x-7)^2-5$
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