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Your Notes Homework Example 2 Use eccentricity to write an equation Write an equation of a hyperbola with center (21, 3), vertex (3, 3), and e 5 3. Solution Use the form (x2h)2 (y2k)2 } 2 } 5 1. The vertex lies a2 b2 3 2 (21) 5 4 units from the center, so a 5 4 . Because e 5 c } a 5 3, you know that c } 5 3, or c 5 12 . 4 So, b2 5 c22a2 5 144 2 16 5 128 . The equation is (x 1 1)2 } 16 2 (y 2 3)2 } 128 5 1. Example 3 Use eccentricity to write a model An asteroid orbits the sun in an elliptical path with the sun at one focus. The eccentricity of the orbit is e 5 0.229 and the length of the major axis is 9.0 astronomical units (A.U). Find an equation of the orbit. (Assume that the major axis is horizontal.) Solution The equation of the orbit has the form x2 y2 } 1 } 5 1. You a2 b2 know that 2a 5 9.0 , or a 5 4.5 . e 5 c } a , so 0.229 5 c } , or c ≈ 1.03. For an ellipse, 4.5 c2 = a22 b2 , so b = Ï } a2 2c2 5 Ï }} (4.5) 2 2 (1.03) 2 ≈ 4.4 So, an equation for the asteroid’s orbit is x2 y2 x2 y2 } 1 } 5 1 or } 1 } 5 1, where x and y are (4.5) 2 (4.4) 2 20 19 measured in A.U. Checkpoint Complete the following exercise. 3. For another asteroid, the eccentricity of the orbit is e = 0.459 and the length of the major axis (horizontal) is 14.8 A.U. Find an equation of the asteroid’s orbit. x2 y2 } 1 } 5 1 55 43 258 9.7 Focus On Graphing Algebra 2 Notetaking Guide Copyright © Holt McDougal. All rights reserved.
Words to Review Give an example of the vocabulary word. Distance formula Focus, foci Circle Radius 1 Vertices y 1 x Midpoint formula Directrix Center Ellipse Copyright © Holt McDougal. All rights reserved. Words to Review Algebra 2 Notetaking Guide 259 1 y 1 Major axis x
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Your Notes 9.1 Apply the Distance a
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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
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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
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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
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Page 51 and 52: Focus On Graphing Use after Lesson
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