Precalculus (6th Edition)

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

Chapter 10 - Analytic Geometry - 10.1 Parabolas - 10.1 Exercises - Page 967: 31

Answer

$$\eqalign{ & {\text{Focus: }}\left( {4,3} \right) \cr & {\text{directrix: }}x = - 2 \cr & {\text{axis of symmetry: }}y = 3 \cr} $$

Work Step by Step

$$\eqalign{ & {\left( {y - 3} \right)^2} = 12\left( {x - 1} \right) \cr & {\text{This equation is written in the form }}{\left( {y - k} \right)^2} = 4p\left( {x - h} \right){\text{ }} \cr & {\text{represents Parabola with horizontal axis of symmetry}} \cr & {\text{of Symmetry and Vertex }}\left( {h,k} \right). \cr & \underbrace {{{\left( {y - 3} \right)}^2} = 12\left( {x - 1} \right)}_{{{\left( {y - k} \right)}^2} = 4p\left( {x - h} \right).} \cr & {\text{Let }}k = 3,\,\,\,\,h = 1 \cr & 4p = 12 \cr & p = 3 \cr & {\text{Focus}}\left( {p + h,k} \right){\text{ and directrix }}x = - p + h \cr & {\text{Axis of symmetry }}y = k \cr & {\text{Focus: }}\left( {3 + 1,3} \right) \cr & {\text{Focus: }}\left( {4,3} \right) \cr & {\text{directrix: }}x = - 3 + 1 \cr & {\text{directrix: }}x = - 2 \cr & {\text{axis of symmetry: }}y = 3 \cr & \cr & {\text{Focus: }}\left( {4,3} \right) \cr & {\text{directrix: }}x = - 2 \cr & {\text{axis of symmetry: }}y = 3 \cr} $$
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