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24.25–30Identify the type of conic section whose equation is givenand find the vertices and foci.22.214.171.124.29.30.31–48Find 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 x2y1x2y21x24y2y2y28y6x16y22y4x234x24xy200, 01, 00, 0y64, 0x23, 63, 22, 31, 51, 01, 13, 12, 05, 00, 50, 130, 20, 60, 00, 80, 18, 19, 11, 41, 01, 64, 04, 1.83, 05, 00, 20, 53, 43, 63, 73, 91, 27, 22, 28, 23, 0y2x2, 02, 8y312xy512xy24x22y16x314x2y224x4y28010.5Exercises1.Homework Hints available at stewartcalculus.com
CONIC SECTIONS70149.The point in a lunar orbit nearest the surface of the moon iscalled periluneand the point farthest from the surface is calledapolune. The Apollo 11spacecraft was placed in an ellipticallunar orbit with perilune altitude 110 km and apolune altitude314 km (above the moon). Find an equation of this ellipse ifthe radius of the moon is 1728 km and the center of the moonis 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 navigationsystem, two radio stations located at and transmit simulta-neous signals to a ship or an aircraft located at . The onboardcomputer converts the time difference in receiving these signalsinto a distance difference , and this, according tothe definition of a hyperbola, locates the ship or aircraft on onebranch of a hyperbola (see the figure). Suppose that station B islocated 400 mi due east of station A on a coastline. A shipreceived the signal from B 1200 microseconds (s) before itreceived the signal from A.(a)Assuming that radio signals travel at a speed of 980 fts,find an equation of the hyperbola on which the ship lies.