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# Calculus: One and Several Variables

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P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY T1: PBU JWDD027-10 JWDD027-Salas-v1 December 2, 2006 16:41 524 SECTION 10.1 CHAPTER 10 SECTION 10.1 1. y = 1 2 x 2 vertex (0 , 0) focus (0 , 1 2 ) axis x = 0 directrix y = 1 2 2. y = 1 2 x 2 vertex (0 , 0) focus (0 , 1 2 ) axis x = 0 directrix y = 1 2 x y x y 3. y = 1 2 ( x 1) 2 vertex (1 , 0) focus (1 , 1 2 ) axis x = 1 directrix y = 1 2 4. y = 1 2 ( x 1) 2 vertex (1 , 0) focus (1 , 1 2 ) axis x = 1 directrix y = 1 2 1 x y 1 x y 5. y + 2 = 1 4 ( x 2) 2 vertex (2 , 2) focus (2 , 1) axis x = 2 directrix y = 3 6. y 2 = 1 4 ( x + 2) 2 vertex ( 2 , 2) focus ( 2 , 3) axis x = 2 directrix y = 1 2 x y -2 x y

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P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY T1: PBU JWDD027-10 JWDD027-Salas-v1 December 2, 2006 16:41 SECTION 10.1 525 7. y = x 2 4 x vertex (2 , 4) focus (2 , 15 4 ) axis x = 2 directrix y = 17 4 8. y = x 2 + x + 1 vertex ( 1 2 , 3 4 ) focus ( 1 2 , 1) axis x = 1 2 directrix y = 1 2 2 x y 1 2 x y 9. x 2 9 + y 2 4 = 1 center (0,0) foci ( ± 5 , 0) length of major axis 6 length of minor axis 4 10. x 2 4 + y 2 9 = 1 center (0,0) foci (0 , ± 5) length of major axis 6 length of minor axis 4 11. x 2 4 + y 2 6 = 1 center (0,0) foci (0 , ± 2) length of major axis 2 6 length of minor axis 4 12. x 2 4 + y 2 3 = 1 center (0,0) foci ( ± 1 , 0) length of major axis 4 length of minor axis 2 3
P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY T1: PBU JWDD027-10 JWDD027-Salas-v1 December 2, 2006 16:41 526 SECTION 10.1 13. x 2 9 + ( y 1) 2 4 = 1 center (0,1) foci ( ± 5 , 1) length of major axis 6 length of minor axis 4 14. x 2 + ( y 3) 2 4 = 1 center (0,3) foci (0 , 3 ± 3) length of major axis 4 length of minor axis 2 15. ( x 1) 2 16 + y 2 64 = 1 center (1,0) foci (1 , ± 4 3) length of major axis 16 length of minor axis 8 16. ( x 2) 2 25 + ( y 3) 2 16 = 1 center (2,3) foci (5 , 3) ( 1 , 3) length of major axis 10 length of minor axis 8 17. x 2 y 2 = 1 center (0,0) transverse axis 2 vertices ( ± 1 , 0) foci ( ± 2 , 0) asymptotes y = ± x 18. y 2 x 2 = 1 center (0,0) transverse axis 2 vertices (0 , ± 1) foci (0 , ± 2) asymptotes y = ± x

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P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY T1: PBU JWDD027-10 JWDD027-Salas-v1 December 2, 2006 16:41 SECTION 10.1 527 19. x 2 9 y 2 16 = 1 center (0,0) transverse axis 6 vertices ( ± 3 , 0) foci ( ± 5 , 0) asymptotes y = ± 4 3 x 20. x 2 16 y 2 9 = 1 center (0,0) transverse axis 8 vertices ( ± 4 , 0) foci ( ± 5 , 0) asymptotes y = ± 3 4 x 21. y 2 16 x 2 9 = 1 center (0,0) transverse axis 8 vertices (0 , ± 4) foci (0 , ± 5) asymptotes y = ± 4 3 x 22. y 2 9 x 2 16 = 1 center (0,0) transverse axis 6 vertices (0 , ± 3) foci (0 , ± 5) asymptotes y = ± 3 4 x 23. ( x 1) 2 9 ( y 3) 2 16 = 1 center (1,3) transverse axis 6 vertices (4 , 3) and ( 2 , 3) foci (6 , 3) and ( 4 , 3) asymptotes y 3 = ± 4 3 ( x 1) 24. ( x 1) 2 16 ( y 3) 2 9 = 1 center (1,3) transverse axis 8 vertices (5 , 3) and ( 3 , 3) foci (6 , 3) and ( 4 , 3) asymptotes y = ± 3 4 ( x 1) + 3
P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY T1: PBU JWDD027-10 JWDD027-Salas-v1 December 2, 2006 16:41 528 SECTION 10.1 25. ( y 3) 2 4 ( x 1) 2 1 = 1 center (1 , 3) transverse axis 4 vertices (1 , 5) and (1 , 1) foci (1 , 3 ± 5) asymptotes y 3 = ± 2( x 1) 26. ( x + 1) 2 y 2 3 = 1 center ( 1 , 0) transverse axis 2 vertices (0 , 0) and ( 2 , 0) foci (1 , 0) and ( 3 , 0) asymptotes y = ± 3( x + 1) 27. We can choose the coordinate system so that the

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