thomasET_226348_ism46

thomasET_226348_ism46 - Section 10.1 Conic Sections and...

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Section 10.1 Conic Sections and Quadratic Equations 619 39. (a) y 8x 4p 8 p 2 directrix is x 2, # œ Ê œÊœÊ œ ± focus is ( ), and vertex is ( 0); therefore the new #ß! directrix is x 1, the new focus is (3 2), and the œ± ß± new vertex is (1 2) 40. (a) x 4y 4p 4 p 1 directrix is y 1, # Ê œ Ê œ Ê œ focus is ( 1), and vertex is ( 0); therefore the new !ß± directrix is y 4, the new focus is ( 1 2), and the ß new vertex is ( 1 3) ±ß 41. (a) 1 center is ( 0), vertices are ( 4 0) x 16 9 y # # ²œÊ ! ß ± ß and ( ); c a b 7 foci are 7 0 %ß! œ ± œ Ê ß È ÈÈ Š‹ ## and 7 ; therefore the new center is ( ), the È ! % ß $ new vertices are ( 3) and (8 3), and the new foci are ß 47 È „ß $ 42. (a) 1 center is ( 0), vertices are (0 5) x 92 5 y # # ! ß ß and (0 5); c a b 16 4 foci are œ ± œ œ Ê È È ( 4) and ( 4) ; therefore the new center is ( 3 2), ± ß± the new vertices are ( 3 3) and ( 3 7), and the new ±ß± foci are ( 3 2) and ( 3 6) 43. (a) 1 center is ( 0), vertices are ( 4 0) x 16 9 y # # ±œÊ ! ß ± ß and (4 0), and the asymptotes are or ßœ x 43 y y ; c a b 25 5 foci are œ„ œ ² œ 3x 4 È È ( 5 0) and (5 0) ; therefore the new center is (2 0), the ß ß new vertices are ( 2 0) and (6 0), the new foci ß are ( 3 0) and (7 0), and the new asymptotes are ß y 3(x 2) 4 ±
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620 Chapter 10 Conic Sections and Polar Coordinates 44. (a) 1 center is ( 0), vertices are (0 2) y 45 x # # ±œÊ ! ß ß ± and (0 2), and the asymptotes are or ßœ y 2 x 5 È y ; c a b 9 3 foci are œ„ œ ² œ œ Ê 2x 5 È È È ## (0 3) and (0 3) ; therefore the new center is (0 2), ßß ± ß ± the new vertices are (0 4) and (0 0), the new foci ß± ß are (0 1) and (0 5), and the new asymptotes are ± y2 ²œ„ 2x 5 È 45. y 4x 4p 4 p 1 focus is ( 0), directrix is x 1, and vertex is (0 0); therefore the new # œ Ê œÊœÊ " ß œ ± ß vertex is ( 2 3), the new focus is ( 1 3), and the new directrix is x 3; the new equation is ±ß± œ± (y 3) 4(x 2) ²œ² # 46. y 12x 4p 12 p 3 focus is ( 3 0), directrix is x 3, and vertex is (0 0); therefore the new # Ê œ Ê œ Ê ± ß œ ß vertex is (4 3), the new focus is (1 3), and the new directrix is x 7; the new equation is (y 3) 12(x 4) œ ± œ ± ± # 47. x 8y 4p 8 p 2 focus is (0 2), directrix is y 2, and vertex is (0 0); therefore the new # ß œ ± ß vertex is (1 7), the new focus is (1 5), and the new directrix is y 9; the new equation is (x 1) 8(y 7) ±œ² # 48. x 6y 4p 6 p focus is , directrix is y , and vertex is (0 0); therefore the new # # œ Ê œ Ê œ Ê œ ± ß 33 3 ˆ‰ vertex is ( 3 2), the new focus is 3 , and the new directrix is y ; the new equation is " 7 (x 3) 6(y 2) # 49. 1 center is ( 0), vertices are (0 3) and ( 3); c a b 9 6 3 foci are 3 x 69 y # # ² œ Ê ß !ß± œ ± œ ± œ Ê È ÈÈ È Š‹ and 3 ; therefore the new center is ( 1), the new vertices are ( 2 2) and ( 4), and the new foci È ±#ß± ± ß are 1 3 ; the new equation is 1 È ±#ß± „ ² œ (x 2) (y 1) ±± 50. y 1 center is ( 0), vertices are 2 and 2 ; c a b 2 1 1 foci are x 2 # ²œÊ ! ß ß !
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thomasET_226348_ism46 - Section 10.1 Conic Sections and...

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