Identify the type of conic section whose equation is given and find the

Identify the type of conic section whose equation is

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24.25–30Identify the type of conic section whose equation is givenand find the vertices and foci. 25. 26. 27. 28. 29. 30. 31–48 Find an equation for the conic that satisfies the given conditions. 31. Parabola, vertex , focus 32. Parabola, focus , directrix 33. Parabola, focus , directrix 34. Parabola, focus , vertex 35. Parabola, vertex , vertical axis, passing through 36. Parabola, horizontal axis, passing through , , and 37. Ellipse, foci , vertices 38. Ellipse, foci , vertices 39. Ellipse, foci , , vertices , 40. Ellipse, foci , , vertex 41. Ellipse, center , vertex , focus 42. Ellipse, foci , passing through 43. Hyperbola, vertices , foci 44. Hyperbola, vertices , foci 45. Hyperbola, vertices , , foci , 46. Hyperbola, vertices , , foci , 47. Hyperbola, vertices , asymptotes 48. Hyperbola, foci , , asymptotes and x 2 y 1 x 2 y 2 1 x 2 4 y 2 y 2 y 2 8 y 6 x 16 y 2 2 y 4 x 2 3 4 x 2 4 x y 2 0 0, 0 1, 0 0, 0 y 6 4, 0 x 2 3, 6 3, 2 2, 3 1, 5 1, 0 1, 1 3, 1 2, 0 5, 0 0, 5 0, 13 0, 2 0, 6 0, 0 0, 8 0, 1 8, 1 9, 1 1, 4 1, 0 1, 6 4, 0 4, 1.8 3, 0 5, 0 0, 2 0, 5 3, 4 3, 6 3, 7 3, 9 1, 2 7, 2 2, 2 8, 2 3, 0 y 2 x 2, 0 2, 8 y 3 1 2 x y 5 1 2 x y 2 4 x 2 2 y 16 x 31 4 x 2 y 2 24 x 4 y 28 0 10.5 Exercises 1. Homework Hints available at stewartcalculus.com
CONIC SECTIONS 701 49. The point in a lunar orbit nearest the surface of the moon is called perilune and the point farthest from the surface is called apolune . The Apollo 11 spacecraft was placed in an elliptical lunar orbit with perilune altitude 110 km and apolune altitude 314 km (above the moon). Find an equation of this ellipse if the radius of the moon is 1728 km and the center of the moon is at one focus. 50. A cross-section of a parabolic reflector is shown in the figure. The bulb is located at the focus and the opening at the focus is 10 cm. (a) Find an equation of the parabola. (b) Find the diameter of the opening , 11 cm from the vertex. 51. In the LORAN (LOng RAnge Navigation) radio navigation system, two radio stations located at and transmit simulta- neous signals to a ship or an aircraft located at . The onboard computer converts the time difference in receiving these signals into a distance difference , and this, according to the definition of a hyperbola, locates the ship or aircraft on one branch of a hyperbola (see the figure). Suppose that station B is located 400 mi due east of station A on a coastline. A ship received the signal from B 1200 microseconds ( s) before it received the signal from A. (a) Assuming that radio signals travel at a speed of 980 ft s, find an equation of the hyperbola on which the ship lies.

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