document.write( "Question 836757: please help me solve this type of problem :A satellite orbits around the earth in an elliptical path of eccentricity 0.6 and semi-minor axis of length 12000 miles. if the center of the earth is at one of the foci,find the maximum altitude of the satelite. \n" ); document.write( "

Algebra.Com's Answer #504356 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "On the graph, we will say the scale 1 unit = 1000 miles.\r\n" );
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document.write( "The equation of the ellipse might be , \r\n" );
document.write( "but we don't need that.\r\n" );
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document.write( "The center of the earth is at point C, one of the focal points of the\r\n" );
document.write( "elliptical orbit of the satellite.  The red circle represents a cross section\r\n" );
document.write( "of the earth.  We assume the radius of the earth is 4000 mile = 4 units.\r\n" );
document.write( "The point S is the surface of the earth where the satellite is at its\r\n" );
document.write( "highest distance above the surface of the earth.\r\n" );
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document.write( "We want to find the length of SA.\r\n" );
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document.write( "OB=b is the semi-minor axis and it is given as 12 units (12000 miles).\r\n" );
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document.write( "The Pythagorean relation for every ellipse is \r\n" );
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document.write( "c²=a²-b²\r\n" );
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document.write( "We are given the eccentricity 0.6 = \r\n" );
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document.write( "So c = OC = 0.6*OA = 0.6a, and we are given b = OB = 12 (12000 miles)\r\n" );
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document.write( "Substituting\r\n" );
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document.write( "So OA = a = 15\r\n" );
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document.write( "and OC = c = 0.6a = .6(15) = 9 = \r\n" );
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document.write( "SC = 4 (radius =4000 mi.)\r\n" );
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document.write( "OS = OC-SC = 9-4 = 5\r\n" );
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document.write( "So SA = OS+OA = 5+15 = 20\r\n" );
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document.write( "So the maximum altitude of the satellite is 20000 miles.\r\n" );
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document.write( "Edwin

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