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Your Notes Example 4 Write an equation of a translated ellipse Write an equation of the ellipse with foci at (22, 3) and (4, 3) and co-vertices at (1, 4) and (1, 2). 1. Determine the form of the y equation. First sketch the ellipse. The foci lie on the major axis, so the axis is (−2, 3) (1, 4) (4, 3) horizontal . The equation (1, 2) 1 has the form: 1 x (x 2 h)2 (y 2 k)2 } 1 } 5 1 a2 b2 2. Identify h and k by finding the center, which is halfway between the foci (or the co-vertices). 22 1 4 3 1 3 (h, k) 5 1 } , } 2 2 2 5 ( 1 , 3 ) 3. Find b, the distance between a co-vertex and the center, and c, the distance between a focus and the center: b 5 ⏐ 4 2 3 ⏐ 5 1 , c 5 ⏐ 22 2 1 ⏐ 5 3. 4. Find a. For an ellipse, a2 5 b2 1 c2 5 12 1 32 5 10 , so a 5 Ï } 10 . The standard form of the equation is (x 2 1)2 } 10 (y 2 3)2 1 } 5 1 . 1 Checkpoint Complete the following exercise. 4. Write an equation of the ellipse with foci at (23, 0) and (23, 26) and co-vertices at (21, 23) and (25, 23). (x 1 3)2 } 4 (y 1 3)2 1 } 5 1 13 Copyright © Holt McDougal. All rights reserved. Lesson 9.6 Algebra 2 Notetaking Guide 251
Your Notes Homework CLASSIFYING CONICS USING THEIR EQUATIONS Any conic can be described by a general second-degree equation in x and y: Ax2 1 Bxy 1 Cy2 1 Dx 1 Ey 1 F 5 0. The expression B2 2 4AC is the discriminant of the conic equation and can be used to identify it. Discriminant Type of Conic B2 2 4AC 0, B 5 0, and A 5 C Circle B2 2 4AC 0 and either B Þ 0 or A Þ C Ellipse B2 2 4AC 0 Parabola B2 2 4AC 0 Hyperbola If B vertical. 0, each axis of the conic is horizontal or Example 5 Classify a conic Classify the conic given by 2x 2 1 2y 2 2 5x 1 3y 2 1 5 0. Solution Note that A 5 , B 5 , and C 5 , so the value of the discriminant is: B2 2 4AC 5 5 . Because B2 2 4AC 0 and A C, the conic is a . Checkpoint Classify the conic. 5. 5x 2 2 3y 2 2 10x 2 12y 2 22 5 0 252 Lesson 9.6 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 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: Your Notes Example 4 Write an equat
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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