thomasET_226348_ism53

# thomasET_226348_ism53 - 676 Chapter 10 Conic Sections and...

This preview shows pages 1–6. Sign up to view the full content.

676 Chapter 10 Conic Sections and Polar Coordinates 50. r 1 sin and r 1 sin 1 sin 1 sin œ± œ² Ê ± )) ) ) 2 sin 0 sin 0 0, ; 0 or Êœ Ê œ Ê œ œ ) 1 ) 1 r 1. The points of intersection are (1 0) and (1 ). ß ß 1 The point of intersection ( 0) is found by graphing. 51. r 1 sin and r 1 sin intersect at all points of œ²± r 1 sin because the graphs coincide. This can be ) seen by graphing them. 52. r 1 cos and r 1 cos intersect at all points of r 1 cos because the graphs coincide. This can be ) seen by graphing them. 53. r sec and r 2 sin sec 2 sin œœ Ê œ ) ) 1 2 sin cos 1 sin 2 2 Ê œÊœ ) ) ) 11 # 4 r 2 sin 2 the point of intersection is œ Ê 1 4 È 2 . No other points of intersection exist. Š‹ È ß 1 4 54. r 2 csc and r 4 cos 2 csc 4 cos Ê ² ) ) 1 2 sin cos 1 2 , Ê œ ) ) ## 5 , ; r 4 cos 2 2 ; œ Ê œ² 1 1 44 4 4 5 È r 4 cos 2 2 . The point of ) œÊ œ ² œ 55 È intersection is 2 2 and the point 2 2 is the Š ÈÈ ß² ß 5 same point.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Chapter 10 Practice Exercises 677 55. r cos 2 3 r cos cos sin sin ˆ‰ ˆ È )) ) ±œ Ê ² 11 1 33 3 2 3 r cos r sin 2 3 œÊ ² œ ÈÈ " ## È 3 r cos 3 r sin 4 3 x 3 y 4 3 Ê² œ Ê ² œ È È yx 4 Êœ ² È 3 3 56. r cos r cos cos sin sin ˆ ) ²œÊ ± 3 44 4 2 1 È # r cos r sin x y 1 ² ± ² ± œ È È 22 2 2 # # yx1 Êœ± 57. r 2 sec r r cos 2 x 2 œ Êœ Ê œ 2 cos ) 58. r 2 sec r cos 2 x 2 œ² Ê Ê œ² È 59. r csc r sin y Ê œ² Ê œ² 3 # 60. r 3 3 csc r sin 3 3 y 3 3 œ Ê œ È
678 Chapter 10 Conic Sections and Polar Coordinates 61. r 4 sin r 4r sin x y 4y 0 œ± Ê Ê ² ² œ )) ## # x (y 2) 4; circle with center ( 2) and Ê ² ² œ !ß± radius 2. 62. r 3 3 sin r 3 3 r sin œÊ œ ÈÈ # xy3 3 y 0 x y ; Ê² ± œ Ê²± œ # # # È Š‹ 33 27 4 È circle with center and radius 63. r 2 2 cos r 2 2 r cos œ # xy2 2 x x 2 y2 ; ± œ Ê ± ² œ # # circle with center 2 0 and radius 2 ß 64. r 6 cos r 6r cos x y 6x 0 Ê Ê # (x 3) y 9; circle with center ( 3 0) and Ê²²œ ± ß radius 3 65. x y 5y 0 x y C # # ²²œÊ ²² œ Êœ ! ß ± ˆ‰ ˆ 52 5 5 4 and a ; r 5r sin 0 r 5 sin œ² œ Ê œ ± 5 # # 66. x y 2y 0 x (y 1) 1 C ( 1) and # # ²±œÊ ²± œÊœ ! ß a 1; r 2r sin 0 r 2 sin œ Ê œ #

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Chapter 10 Practice Exercises 679 67. x y 3x 0 x y C ## # # ±²œÊ ² ±œÊœß ! ˆ‰ ˆ 39 3 4 and a ; r 3r cos 0 r 3 cos œ² œ Ê œ 3 # # )) 68. x y 4x 0 (x 2) y 4 C ( 2 0) ±±œÊ ± ±œÊœ² ß and a 2; r 4r cos 0 r 4 cos œ± œ Ê œ ² # 69. r e 1 parabola with vertex at (1 0) œÊ œ Ê ß 2 1c o s ± ) 70. r r e ellipse; œ Ê œ Ê 84 2c o s 1 c o s ±# ± " ) ) " # ke 4 k 4 k 8; k ea 8 a œÊ œÊœ œ²Êœ ² "" aa e " # a ea ; therefore the center is Êœ Ê œ œ 16 16 8 33 3 ˆ‰ˆ ‰ " # ; vertices are ( ) and 0 88 ß) ß ß 11 71. r e 2 hyperbola; ke 6 2k 6 œ ÊœÊ œÊ œ 6 12 c o s ² ) k 3 vertices are (2 ) and (6 ) ß ß 72. r r e ; ke 4 œ Ê œ œ 12 4 3s i n 3 s i n ± ± " ) ) " 3 k 4 k 12; a 1 e 4 a 1 Êœ Ê œ ² œ Ê ² # # ab ’“ 4 a ea ; therefore the œÊœÊ œ œ 99 3 3 # " ˆ‰ˆ‰ center is ; vertices are 3 and 6 ˆ ˆ ‰ˆ‰ 3 # # ßß ß 1 73. e 2 and r cos 2 x 2 is directrix k 2; the conic is a hyperbola; r r œ œÊœ œ ) ke 1 e cos 1 cos (2)(2) ±± # r 4 c o s )
680

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

### Page1 / 17

thomasET_226348_ism53 - 676 Chapter 10 Conic Sections and...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online