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CHAPTER 9 Topics in Analytic Geometry Section 9.1 Circles and Parabolas ■ A parabola is the set of all points x, y that are equidistant from a fixed line (directrix) and a fixed point (focus) not on the line. ■ The standard equation of a parabola with vertex h, k and (a) Vertical axis x h and directrix y k p is (x h) 2 4p( y k), p 0. (b) Horizontal axis y k and directrix x h p is (y k) 2 4p(x h), p 0. ■ The tangent line to a parabola at a point P makes equal angles with (a) the line through P and the focus. (b) the axis of the parabola. Vocabulary Check 1. conic section 2. locus 3. circle, center 4. parabola, directrix, focus 5. vertex 6. axis 7. tangent 1. x 2 y 2 18 2 2. x 2 y 2 18 x 2 y 2 42 2 x 2 y 2 32 3. 5. 7. Radius 3 1 2 7 0 2 4. Radius 6 2 2 3 4 2 4 49 53 64 49 113 x h 2 y k 2 r 2 x h 2 y k 2 r 2 x 3 2 y 7 2 53 x 6 2 y 3 2 113 Diameter 27 ⇒ radius 7 6. Diameter 43 ⇒ radius 23 x h 2 y k 2 r 2 x h 2 y k 2 r 2 x 3 2 y 1 2 7 x 5 2 y 6 2 12 x 2 y 2 49 8. x 2 y 2 1 9. x 2 2 y 7 2 16 Center: 0, 0 Center: 0, 0 Center: 2, 7 Radius: 7 Radius: 1 Radius: 4 © Houghton Mifflin Company. All rights reserved. 772
Section 9.1 Circles and Parabolas 773 10. x 9 2 y 1 2 36 11. x 1 2 y 2 15 12. x 2 y 12 2 24 Center: 9, 1 Center: 1, 0 Center: 0, 12 Radius: 6 Radius: 15 Radius: 24 26 13. 1 4 x2 1 4 y2 1 14. 1 9 x2 1 9 y2 1 15. 4 3 x2 4 3 y2 1 x 2 y 2 4 Center: 0, 0 Radius: 2 x 2 y 2 9 Center: 0, 0 Radius: 3 x 2 y 2 3 4 Center: 0, 0 Radius: 3 2 16. 9 2 x2 9 2 y2 1 17. x 2 y 2 2 9 x 2 2x 1 y 2 6y 9 9 1 9 Center: x 1 2 y 3 2 1 1, 3 Center: 0, 0 Radius: 2 3 Radius: 1 18. x 2 10x 25 y 2 6y 9 25 25 9 19. x 5 2 y 3 2 9 Center: 5, 3 Radius: 3 4x 2 3x 9 4 4y 2 6y 9 41 9 36 Center: Radius: 1 4x 3 2 2 4y 3 2 4 x 3 2 2 y 3 2 1 3 2 , 3 20. 9 x 2 6x 9 9y 2 4y 4 17 81 36 9x 3 2 9y 2 2 100 © Houghton Mifflin Company. All rights reserved. 21. Center: Radius: 10 3 x 2 y 2 16 Center: 0, 0 Radius: 4 x 3 2 y 2 2 100 9 3, 2 y x 2 16 y 2 22. 5 3 2 1 −5 −3 −2 −1 1 2 3 5 −2 −3 −5 x x 2 y 2 81 Center: 0, 0 Radius: 9 y 2 81 x 2 10 8 6 4 2 −10 −6 −4 −2 2 4 6 8 10 −4 −6 −8 −10 y x
Page 1: CHAPTER 9 Topics in Analytic Geomet
Page 5 and 6: Section 9.1 Circles and Parabolas 7
Page 15 and 16: Section 9.2 Ellipses 785 4. x 2 4
Page 17 and 18: Section 9.2 Ellipses 787 16. (a) 9x
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Page 21 and 22: Section 9.2 Ellipses 791 36. Center
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Page 25 and 26: Section 9.3 Hyperbolas 795 67. Arit
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) Review Exercises for Chapter 9 87
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