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Your Notes Example 1 Graph an equation of an ellipse Graph the equation 9x2 1 36y2 5 324. Identify the vertices, co-vertices, and foci of the ellipse. 1. Rewrite the equation in standard form. 9x2 1 36y2 5 324 Write original equation. 9x2 } 342 x2 } 36 1 36y2 } 324 1 y2 } 9 5 324 } 324 5 1 Simplify. 2. Identify the vertices, co-vertices, and foci. Note that a 2 5 36 and b 2 5 9 , so a 5 6 and b 5 3 . The denominator of the x 2 -term is greater than that of the y 2 -term, so the major axis is horizontal . The vertices of Divide each side by 324 . (− 27, 0) (−6, 0) 2 (0, −3) y (0, 3) 2 ( 27, 0) the ellipse are at (6a, 0) 5 (6 6 , 0). The co-vertices are at (0, 6b) 5 (0, 6 3 ). Find the foci. c2 5 a2 2 b2 5 62 2 32 5 27 , so c 5 Ï } 27 . The foci are at (6 Ï } 27 , 0), or about (6 5.2 , 0). x (6, 0) 3. Draw the ellipse that passes through each vertex and co-vertex. Example 2 Write an equation given a vertex and a co-vertex Write an equation of the ellipse that has a vertex at (0, 7), a co-vertex at (24, 0), and center at (0, 0). Sketch the ellipse as a check for your final equation. By symmetry, the (0, 7) y ellipse must also have a vertex at (0, 27 ) and a co-vertex at ( 4 , 0). Because the vertex is on the y-axis (4, −0) 2 2 (4, 0) x and the co-vertex is on the x-axis , the major axis is vertical with (0, −7) a 5 7 , and the minor axis is horizontal with b 5 4 . An equation is x2 } 4 y2 x2 1 } 5 1, or } 2 2 7 16 1 y2 } 49 5 1. 242 Lesson 9.4 Algebra 2 Notetaking Guide Copyright © Holt McDougal. All rights reserved.
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 , the major axis is , with a 5 and c 5 . To find b, use the equation c 2 5 a 2 2 b 2 . 5 2 b 2 b 2 5 2 5 b 5 An equation is 5 1, or 5 1. Checkpoint Graph the equation. Identify the vertices, co-vertices, and foci of the ellipse. 1. x2 1 y2 } 5 1 25 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) Copyright © Holt McDougal. All rights reserved. Lesson 9.4 Algebra 2 Notetaking Guide 243 2 2 y y 2 2 x x
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
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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
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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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