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Soal No 17 halaman 66

Soal No 17 halaman 66. Find a) the coordinates of the foci and vertices for hyperbola whose equations given, b) equation of the asymptotes. Sketch the curve. Penyelesaian :. Jelas Titik puncak adalah P( a,0) dan Q(-a,0) Jadi titik puncaknya adalah P(8,0) dan Q(-8,0). Jelas

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Soal No 17 halaman 66

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  1. Soal No 17 halaman 66 Find a) the coordinates of the foci and vertices for hyperbola whose equations given, b) equation of the asymptotes. Sketch the curve.

  2. Penyelesaian: Jelas Titikpuncakadalah P( a,0) dan Q(-a,0) Jadititikpuncaknyaadalah P(8,0) dan Q(-8,0)

  3. Jelas Foci diperolehdari (c,0) dan (-c,0). Jadifocinyaadalah

  4. Persamaanasimtotdarihyperbola Dapatdiperolehdari

  5. Gambargrafiknya

  6. Nomor 21 Halaman 66 Sketch the two equation of each system on the same set of axes and specify the number of real number of the system.

  7. Penyelesaian Jelaspersamaan (1) adalahpersamaanlingkarankarena A=B denganpanjangjari-jari 3. Jelaspersamaan (2) adalahpersamaanhiperbola, karenatanda A tidaksamadengantanda B dan

  8. JelasPersamaan (2) : Titikpuncak P(a,0) dan Q(-a,0). Jadititikpuncaknya P(2,0) dan Q(-2,0). Jelas foci diperolehdari (c,0) dan (-c,0) sehingga Jadifocinyaadalah

  9. Gambargrafiknya

  10. Exercise 2.4 number 27 Find a standard equation of the hyperbola that has the foci of ellips 9x + 4y = 36 for vertices and the vertices of the ellips for foci.

  11. Persamaan elips 9x + 4y = 36 Persamaan tersebut dapat dibentuk menjadi persamaan baku dari ellips dengan kedua ruas dikalikan , diperoleh: Ingat : Ada 2 bentuk persamaan ellipsatau

  12. Jelas sehinggapersamaanberbentuk dengan fokus pada sumbu Y. Dari persaman tersebut diperoleh dan Nilai a menunjukkanabsiskoordinat titik puncak pada sumbu Y. Jadi diperoleh koordinat titik puncaknya adalah

  13. Untuk mencari fokus dapat dapat diperoleh dengan mensubstitusikan nilai a = 3 dan b = 2 dalam persamaan maka diperoleh:

  14. Nilai c menunjukkan ordinatkoordinat titik fokus pada sumbu Y jadi fokusnya Karena titik puncak elips merupakan titik fokus hiperbola dan titik fokus elips merupakan titik puncak hiperbola maka titik fokus hiperbola adalah dan titik puncak hiperbola adalah

  15. Mencaripersamanhiperbola Substitusikan dan ke persamaan , maka diperoleh Jadipersamaanhiperbola

  16. Soal No 28 Halaman 66 Find the length of the perpendicular segment from a focus of the hyperbola to one of the asymptotes. Answer From the equations, we get the foci of hyperbola are M(0,c) and N(0,-c) So one of the focus is P

  17. The asymptote of the equation is So the coordinate of the asymptote (b,a) The length of the perpendicular segment from a focus of hyperbola and one of the asymptote is

  18. Nomor 19 Halaman 70 Name and sketch the graph of each equation Solution : Because of A and C same sign, B=0 so the name of graph from the equation is two parallel lines.

  19. Sketch of the Graph

  20. Soal No 22 Halaman 70 Graph the set of points contained in the graphs of • Both and • Either or

  21. Penyelesaian Jelasadalahpersamaanlingkarankarena A=B, denganpanjangjari-jari 6. Jelasadalahpersamaan parabola. Jika x= 0 maka y= -6 x=1 maka y= -5 x=-1 maka y= -5 x=2 maka y= -2 x=-2 maka y=-2

  22. The graph of 22 a

  23. The graph of 22 b

  24. Nomor 24 Halaman 70 Graph each pair of conjugate hyperbola Solution

  25. Persamaan 1 Jelas Titikpuncakdarihiperboladiperolehdari P(0,a) and Q(0,-a) Jelas JadititikpuncaknyaadalahP(0, 3) and Q (0,-3)

  26. Foci darihiperboladiperolehdari (0,c) dan (0,-c). Jelas Jadifocinyaadalah

  27. Persamaan 2 Jelas TitikpuncakdarihiperboladiperolehdariA(a,0) dan B (-a,0) Jelas JadititikpuncaknyaadalahA(2,0) dan B(-2,0)

  28. Foci darihiperboladiperolehdari(0,c) dan (0,-c). Jelas Jadifocinyaadalah

  29. Gambargrafiknya

  30. Hal 70 no.25 Show that the foci of the conjugate hyperbolas and lie on circle. Solution A hyperbola has the standard equation From , we get Foci of are A(0,c) and B(0,-c)

  31. From , we also get Foci of is M(0,c) and N(0,-c) So for both hyperbolas and And A=B, hence all foci are equidistant from a common point (the origin) and therefore lie on a circle

  32. Hal 66 no.29 By solving for y, obtain the equation and argue that the graph of the equation approaches the stright line graphs of as increases.

  33. Solution As grows larger and larger, approaches 0 and Approaches 1, from which y approaches Jelas

  34. Hal 66 no.30 By solving for x, obtain the equation and argue that the graph of the equation approaches the stright line graphs of as increases.

  35. Solution As grows larger and larger, approaches 0 and Approaches 1, from which x approaches Jelas

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