Chapter 10. Homework

Transcription

1 Chapter 0 Homework

2 Lesson 0- pages Exercises. 2. Hyperbola: center (0, 0), y-intercepts at ±, no x-intercepts, the lines of symmetry are the x- and y-axes; domain: all real numbers, range: y or y < > Ellipse: center (0, 0), x-intercepts at ±3 2, y-intercepts at ±6, the lines of symmetry are the x- and y-axes; domain: 3 2 < x < 3 2, range 6 < y <

3 Lesson Circle: center (0, 0), radius, x-intercepts at ±, y-intercepts at ±, there are infinitely many lines of symmetry; domain: < x <, range: < y <. 6. Ellipse: center (0, 0), y-intercepts at ±2, x-intercepts at ±5, the lines of symmetry are the x- and y-axes; domain: 5 < x < 5, range: 2 < y < 2. Hyperbola: center (0, 0), y-intercepts at ± 3, no x-intercepts, the lines of symmetry are the x- and y-axes; domain: all real numbers, range: y < 3 or y > 3. Circle: center (0, 0), radius 7, x- and y-intercepts at ±7, there are infinitely many lines of symmetry; domain: 7 < x < 7, range: 7 < y < 7. 3

4 Lesson Hyperbola: center (0, 0), y-intercepts at ±, the lines of symmetry are the x- and y-axes; domain: all real numbers, range: y < or y >. 0. Circle: center (0, 0), radius 0, x- and y-intercepts at ±0, there are infinitely many lines of symmetry; domain: 0 < x < 0, range: 0 < y < 0. Circle: center (0, 0), radius 2, x- and Hyperbola: center (0, 0), x-intercepts y-intercepts at ±2, there are infinitely at ±2, the lines of symmetry are the many lines of symmetry; domain: x- and y-axes; domain: x < 2 or x > 2, 2 < x < 2, range: 2 < y < 2. range: all real numbers. 0-

5 Lesson Ellipse: center (0, 0), x-intercepts at ±, y-intercepts at ±2, the lines of symmetry are the x- and y-axes; domain: < x<, range: 2 < y< 2. Ellipse: center (0, 0), x-intercepts at ±, 3 y-intercepts at ±, the lines of symmetry are the x- and y-axes; domain: 3 3 < x <, range: < y <. Circle: center (0, 0), radius 5, x- and y-intercepts at ± 5, there are infinitely many lines of symmetry; domain: 5 < x < 5, range: 5 < y <

6 Lesson Hyperbola: center (0, 0), x-intercepts at ±6, the lines of symmetry are the x- and y-axes; domain: x < 6 or x > 6, range: all real numbers. Hyperbola: center (0, 0), y-intercepts at ±, the lines of symmetry are the x- and y-axes; domain: all real numbers, range: y < or y >. Ellipse: center (0, 0), x-intercepts at ±2, y-intercepts at ±6, the lines of symmetry are the x- and y-axes; domain: 2 < x < 2, range: 6 < y < center (0, 0), x-intercepts at ±3, y-intercepts at ±2; domain: 3 < x < 3, range: 2 < y <

7 Lesson 0-8. center (0, 0), no x-intercepts, y-intercepts at 2; domain: all real numbers, range: y < 2 or y > 2 9. center (0, 0), x-intercepts at 3, no y-intercepts; domain: x < 3 or x > 3, range: all real numbers 20. center (0, 0), x-intercepts at 8, y-intercepts at ; domain: 8 < x < 8, range: < y < 2. center (0, 0), x-intercepts at 3, y-intercepts at 5; domain: 3 < x < 3, range: 5 < y < center (0, 0), no x-intercepts, y-intercepts at 3; domain: all real numbers; range: y < 3 or y > Hyperbola: center (0, 0), x-intercepts ±, the lines of symmetry are the x- and y-axes; domain: x < or x >, range: all real numbers. 7

8 Lesson (0, 0), (6, 0), x = (0, 0), (3, 0), x = (0, 0), (0, ), y = 25. (0, 0), (0, ), y = (0, 0),, 0, x = (0, 0), (0, ), y = 8

9 Lesson (2, 0), (2, ), y = ( 2, ), 2,, y = 5 3. (, 0), (, 6), y = 6 3. (0, 0), ( 2, 0), x = ( 3, 0),, 0, x = (3, ), (6, ), x =

10 36. x = 37. y = 38. y = 39. x = 0. x =. y = 2. Lesson x =. y = 5. x =

11 Lesson ( 6, 0), 25. ( 2, ), (3, 7),

12 Lesson 0-3 pages Exercises. + = (x + ) 2 + (y + 6) 2 = 9 3. (x 2) 2 + (y 3) 2 = (x + 6) 2 + (y 0) 2 = 5. (x ) 2 + (y + 3) 2 = (x + 5) 2 + (y + ) 2 = (x + 3) 2 + = 6 8. (x +.5) 2 + (y + 3) 2 = 9. + (y + ) 2 = 9 0. (x + ) 2 + =. (x 2) 2 + (y + ) 2 = (x + ) 2 + (y 3) 2 = (y + 5) 2 = 00. (x 3) 2 + (y 2) 2 = 9 5. (x + 6) 2 + (y ) 2 = (x 5) 2 + = (x + 3) 2 + (y ) 2 = 9 8. (x 2) 2 + (y + 6) 2 = 6 9. (, ), 20. ( 2, 0), 2 2. (3, ), ( 3, 5), (0, 3),

13 Lesson (0, ), 66. parabola; x = (y + 2) 2 + 3; 59. ( 5, 0), ( 2, ), ( 3, 5), (, 0), (3, ), 6 6. (0, 2), circle; (x ) 2 + (y 3) 2 = 6; 67. Let P(x, y) be any point on the circle centered at the origin and having radius r. If P(x, y) is one of the points (r, 0), ( r, 0), (0, r), or (0, r), substitution shows that + = r 2. If P(x, y) is any other point on the circle, drop a perpendicular PK from P to the x-axis (K on the x-axis). OPK is a right triangle with legs of lengths x and y and with hypotenuse of length r. By the Pythagorean Theorem, x 2 + y 2 = r 2. But x 2 = and y 2 =. So + = r

14 Lesson 0- pages Exercises. + = = 3. + = 9. + = 5. + = = = = = = 6. + = = = = = = = (0, 5), (0, 5) 9. (0, ), (0, )

15 Lesson ( 2, 0), ( 2, 0) 22. (0, 6), (0, 6) 2. (2 3, 0), ( 2 3, 0) 2. (8, 0), ( 8, 0) 23. (0, 6), (0, 6) 25. (9, 0), ( 9, 0) 5

16 Lesson (3 5, 0), ( 3 5, 0) = = = = = = ( 5, 0), ( 5, 0) 3. (0, 2 3), (0, 2 3) 35. (0, 2), (0, 2) 36. (0, 2), (0, 2) 37. (0, 2 7), (0, 2 7) 38. (0, ), (0, ) 39. ( 3, 8), ( 3, 2) 0. ( 2, 2), ( 2, 2) 0-. a. 0.9; b. 0.; c. The shape is close to a circle. d. The shape is close to a line segment. 6

17 Lesson = a. Yes; since c 2 = a 2 b 2, if the foci are close to 0, then c 2 will be close to 0 and a 2 will be close to b 2. This means a will be close to b and hence the ellipse will be close to a circle. b.if F and F 2 are considered distinct pts., then a circle is not an ellipse. If F and F 2 are the same pt., then a circle is an ellipse.. + = = = = 8. The vertices are the points farthest from the center and the co-vertices are the points closest to the center. 9. Check students work = 5. + = = = = =

18 Lesson 0-5 pages Exercises

19 Lesson (0, 3), (0, 3) (0, 97), (0, 97) 2. ( 265, 0), ( 265, 0) 0-5 9

20 Lesson = 20. = 2. = 22. = 23. = 9 69,69 20, = 25. = 26. = 96,80 0,000 92,32,38 70,203, = =

21 Lesson 0-6 pages Exercises (x + 2) 2 (y ) 2 9 (x 5) 2 (y 3) (y + ) (x 3) 2 (y + 6) (x + 3) 2 (y + 3) (y + 3) 2 (x ) 2 32 (x + ) 2 (y 2) (y + ) 2 (x + ) (y ) = 2. + = 3. + =. + = 5. = 6. = 7. = 8. = 9. = (x 50) = (x 75) ,20. = 28, y = (x ) 2 + 3; parabola, vertex (, 3) 3. (x + 6) 2 + = 8; circle, center ( 6, 0), radius

22 Lesson 0-6 (x + ) 2 (y 3) 2. + = ; ellipse, 3 9 center (, 3), foci (, 3 ± 6 ) 6. (y 2) 2 (x 3) 2 = ; hyperbola, center (3, 2), foci (3, 2 ± 2) 5. (x ) 2 + (y + 3) 2 = 3; circle, center (, 3), radius 3 (x ) 2 7. (y + ) 2 = ; hyperbola, center (, ), foci ( ± 5, )

23 Lesson (y + 7) 2 = 36; circle, center (0, 7), radius 6 (x + 2) 2 (y 3) = ; ellipse, center ( 2, 3), foci ( 2 ± 5, 3) 2 9. x 3 = (y 2) 2 ; parabola, vertex (3, 2) 2. (x + 3) 2 (y 5) 2 = ; hyperbola, center ( 3, 5), foci ( 3 ± 2, 5)

24 Lesson 0-6 (x ) = ; ellipse, center (, 0), foci ( ± 2 3, 0) 23. = ; hyperbola, (y + 3) 2 9 center (0, 3), foci (± 3, 3) 2. Translate the equation =, a hyperbola centered at (0, 0), 3 units left. 25. a. hyperbola b. line 26. a. h is added to each x-coordinate, and k is added to each y-coordinate. b. The lengths of the major and minor axes are unchanged; the x-coordinates of the vertices are increased (or decreased) by the same amount, and the same is true for the y-coordinates. A similar remark holds for the co-vertices