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Tugas Terstruktur 4 (P arabolas , Circles , and Ellipses )

Presented by: Kelompok 4 Ihda Mardiana H. Hesti Setyoningsih Dewi Kurni y ati Belynda Surya F. Tugas Terstruktur 4 (P arabolas , Circles , and Ellipses ). No 37 hal 52. Given the function defined by find the equation defining and graph and on the same set of axes

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Tugas Terstruktur 4 (P arabolas , Circles , and Ellipses )

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  1. Presented by: Kelompok 4 • Ihda Mardiana H. • Hesti Setyoningsih • Dewi Kurniyati • Belynda Surya F. Tugas Terstruktur 4 (Parabolas, Circles, and Ellipses)

  2. No 37 hal 52 Given the function defined by find the equation defining and graph and on the same set of axes Diketahui: y= x2, (x ≥ 0) Ditanya:f -1 dan sketsagrafik f dan f -1 pada sumbu yang sama. Penyelesaian: Jelas Jadisupayamenjadifungsimakadipilih

  3. Sketsagrafiknya

  4. No 39 hal 53 If and are two points on the parabola show that the line has the intercept . Solution: Jika dan merupakantitik-titikpada parabola, maka dan . Persamaangarisnyayaitu dimana

  5. Untuk perpotonganterhadapsumbu x, , dankitaperoleh: Substitusikan dan padapersamaan, didapat:

  6. No 10 hal 58 Find the standart equation of the ellips having its center at the origin and meeting the given conditions. One vertex at (0,6) and containing ( Solution: Vertexnya(0,6) berarti a=6 Karena vertexnyaterletak pada sumbu y makafocinyajugaterletakpadasumbu y. Jadi, kitadigunakanteorema 2.6

  7. Jadi,persamaan bakuelipsnya

  8. no 13 hal58 Find the standart equation of the ellips having its center at the origin and meeting the given conditions. One focus at (-4,0) and containing ( Answer: Salah satu fokus adalah (-4,0) berarti c=4Jarak fokus terhadap titik (3,1)adalah:

  9. Karena focinyaterletak pada sumbu x, maka digunakan Teorema 2.5 Jadi, persamaannya sehingga:

  10. No 14 hal 58 Find the standart equation of the ellips having its center at the origin and meeting the given conditions. Length of major axis 12, length of minor axis 8, and foci on the y axis Solution: Panjangsumbu mayor = 12 maka a = 6Panjangsumbu minor = 8 maka b = 4 Karenafokusnyaterletakpadasumbu y, makadigunakanteorema 2.6

  11. No 15 hal 58 Find the coordinates of the foci and vertices of the ellipse with the equation , and sketch the curve. Solution: Persamaandiatasmemenuhiteorema 2.5 dengan a=4 dan b=2 Diperoleh Jadi, vertexnya (-4,0) dan (4,0) danfocinya ( dan )

  12. ( 0,2 ) ( -4,0 ) ( 4,0 ) F1() ( 0,0 ) F2() ( 0,-2 )

  13. No 21 hal 59 Find the coordinates of the foci and vertices of the ellipse with the equation, and sketch the curve Solution: Jelas Dari persamaan di atasdiperoleh a=4 dan b=2 Jadi, vertexnya(0,-4) dan(0,4) danfocinya ( dan

  14. Y (0,4) F1() X ( 0,0 ) (-2,0) (2,0) F2() (0,-4)

  15. No 23 hal 59 Find the eccentricity of the ellipse obtained in problem 15: Answer: Diperolehdan

  16. No 31 hal 59 Find an equation of an ellipse with the foci at (0,3) and (0,-3) if Answer: Diketahui: foci= (0,3) dan(0,-3), berarti c=3, dan Sehingga Karena foci terletakpadasumbu y, gunakanteorema 2.6 Jadipersamaannya

  17. No 32 hal59 Find an equation of the ellipse that contains the point and has foci at (4,0) and (-4,0) Solution: Jarak fokus terhadap titik (3,-12/5)yaitu:

  18. Focinya (4,0) and (-4,0), berarti c=4, sehingga Karena focinyapadasumbu x makakitamenggunakanteorema 2.5 Jadi, persamaanbakunya

  19. No 40 hal 53 Find an equation of the line containing the line segment with endpoints on the parabola that bisected by the point (4,2)

  20. TERIMA KASIH… ^_^

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