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Your Notes Homework Example 3 Write an equation given a vertex and a focus Write an equation of the ellipse that has a vertex at (26, 0) and a focus at (5, 0). Solution Make a sketch of the ellipse. Because the vertex and focus lie on the x-axis , the major axis is horizontal , with a 5 6 and c 5 5 . To find b, use the equation c 2 5 a 2 2 b 2 . 5 2 5 6 2 2 b 2 b2 5 62 2 52 5 11 b 5 Ï } 11 An equation is x2 } 6 1. x2 1 y2 } 5 1 25 (−6, 0) y2 x2 1 } 5 1, or } 2 2 ( Ï } Copyright © Holt McDougal. All rights reserved. Lesson 9.4 Algebra 2 Notetaking Guide 243 11 ) 2 y 2 (6, 0) x (0, 5) (0, −5) 36 1 y2 } 11 ( 0, 24) 2 (−1, 0) 5 1. Checkpoint Graph the equation. Identify the vertices, co-vertices, and foci of the ellipse. vertices: (0, 65) co-vertices: (61, 0) foci: (0, 64.90) ( 0, − 24) y (0, 5) (1, 0) 2 (0, −5) Checkpoint Write an equation of the ellipse with the given characteristics and center at (0, 0). 2. Vertex: (29, 0) 3. Vertex: (0, 7) Co-vertex: (0, 4) Focus: (0, 23) x2 } 81 1 y2 } 16 5 1 x2 } 40 y2 1 } 5 1 49 x
Your Notes 9.5 Graph and Write Equations of Hyperbolas Goal p Graph and write equations of hyperbolas. VOCABULARY Hyperbola Foci Vertices Transverse Axis Center STANDARD EQUATION OF A HYPERBOLA WITH CENTER AT THE ORIGIN Equation Transverse Axis Asymptotes Vertices x2 y2 } 2 } 2 a y2 x2 2 } 2 5 1 Horizontal y 5 6 x (6 , 0) b2 } 5 1 a b2 Vertical y 5 6 x (0, 6 ) The foci lie on the transverse axis, c units from the center, where c2 5 . 244 Lesson 9.4 Algebra 2 Notetaking Guide Copyright © Holt McDougal. All rights reserved.
Page 1 and 2: Your Notes 9.1 Apply the Distance a
Page 3 and 4: Your Notes Checkpoint Complete the
Page 5 and 6: Your Notes Homework Example 4 Find
Page 7 and 8: Your Notes 9.2 Graph and Write Equa
Page 9 and 10: Your Notes Example 1 Graph an equat
Page 11 and 12: Your Notes Homework Example 2 Write
Page 15 and 16: Your Notes Checkpoint Graph the equ
Page 17 and 18: Your Notes Homework Example 4 Write
Page 23: Your Notes Homework Example 3 Write
Page 29 and 30: Your Notes Example 2 Write an equat
Page 31 and 32: Your Notes Homework Example 3 Solve
Page 33 and 34: Your Notes 9.6 Translate and Classi
Page 35 and 36: Your Notes Example 1 Graph the equa
Page 37 and 38: Your Notes Write an equation of the
Page 39 and 40: Your Notes Example 4 Write an equat
Page 41 and 42: Your Notes Homework CLASSIFYING CON
Page 43 and 44: Your Notes 9.7 Solve Quadratic Syst
Page 45 and 46: Your Notes Example 2 Solve a linear
Page 47 and 48: Your Notes Example 3 Solve a quadra
Page 49 and 50: Your Notes Homework Example 4 Solve
Page 51 and 52: Focus On Graphing Use after Lesson
Page 53 and 54: Your Notes Homework Example 2 Use e
Page 55 and 56: Words to Review Give an example of
Page 57 and 58: Co-vertices Hyperbola 2 Conic secti

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