12.5E: Sehemu za Conic katika Kuratibu Polar (Mazoezi)

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Kwa mazoezi yafuatayo, kutokana na equation ya polar ya conic na kuzingatia asili, kutambua eccentricity na directrix.

41. \(r=\frac{10}{1-5 \cos \theta}\)

42. \(r=\frac{6}{3+2 \cos \theta}\)

43. \(r=\frac{1}{4+3 \quad \sin \theta}\)

44. \(r=\frac{3}{5-5} \sin \theta\)

Kwa mazoezi yafuatayo, graph conic iliyotolewa katika fomu ya polar. Ikiwa ni parabola, lebo kipeo, lengo, na directrix. Ikiwa ni ellipse au hyperbola, lebo alama na foci.

45. \(r=\frac{3}{1-\sin \theta}\)

46. \(r=\frac{8}{4+3} \sin \theta\)

47. \(r=\frac{10}{4+5 \cos \theta}\)

48. \(r=\frac{9}{3-6 \quad \cos \theta}\)

Kwa mazoezi yafuatayo, kutokana na taarifa kuhusu grafu ya conic na kuzingatia asili, pata equation katika fomu ya polar.

49. Directrix ni\(x=3\) na eccentricity\(e=1\)

50. Directrix ni\(y=-2\) na eccentricity\(e=4\)