document.write( "Question 117291: Graph the ellipse and find the coordinates of the center vertices and foci.\r
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Algebra.Com's Answer #86108 by Edwin McCravy(20060) $\"\"$ $\"About$
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document.write( "Graph the ellipse and find the coordinates of the center \r\n" );
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document.write( " = 400\r\n" );
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document.write( "equations of the form  have their center at the\r\n" );
document.write( "origin.  So the center is (0,0)\r\n" );
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document.write( " = 400\r\n" );
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document.write( "We want to get this either to the form\r\n" );
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document.write( " = 1 or  = 1\r\n" );
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document.write( "The first one is shaped like an egg sitting on a table.\r\n" );
document.write( "The second one has the shape of the number zero, like this \" 0 \".\r\n" );
document.write( "We will know which form it is in because  is always larger\r\n" );
document.write( "than .\r\n" );
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document.write( " = 400\r\n" );
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document.write( "Get 1 on the right by dividing through by 400:\r\n" );
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document.write( " = \r\n" );
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document.write( " = 1\r\n" );
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document.write( "The larger denominator on the left side is 25,\r\n" );
document.write( "so a² = 25, the smaller denominator of the left\r\n" );
document.write( "is 16, so b² = 16.\r\n" );
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document.write( "So this graph is in the form  = 1\r\n" );
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document.write( "and it will have the shape of a 0.\r\n" );
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document.write( "Since a² = 25, a = 5, Since b² = 16, b = 4\r\n" );
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document.write( "The center is at the origin.\r\n" );
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document.write( "One half the major axis extends from (0,0) to (0,5),\r\n" );
document.write( "and the other half extends from (0,0) to (0,-5).\r\n" );
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document.write( "One half the minor axis extends from (0,0) to (4,0),\r\n" );
document.write( "and the other half extends from (0,0) to (-4,0).\r\n" );
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document.write( "So we draw an upright rectangle through those four \r\n" );
document.write( "points, like this:\r\n" );
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document.write( "Draw an upright ellipse just fitting in that rectangle,\r\n" );
document.write( "shaped like a zero \"0\":\r\n" );
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document.write( "It's vetices are the \"bluntest\" points on the ellipse.\r\n" );
document.write( "They are (0,5) and (0,-5)\r\n" );
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document.write( "Erase the rectangle:\r\n" );
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document.write( "Now we calculate the value of c which in the distance\r\n" );
document.write( "from the center to the foci.  You can remember what\r\n" );
document.write( "c is by noticing that the words \"focus\", \"foci\", and\r\n" );
document.write( "\"center\" contain the letter \"c\".\r\n" );
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document.write( "The formula is c² = a² - b²\r\n" );
document.write( "               c² = 25 - 16\r\n" );
document.write( "               c² = 9\r\n" );
document.write( "                c = \r\n" );
document.write( "                c = 3\r\n" );
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document.write( "So the foci are at (0,3) and (0,-3) marked below with\r\n" );
document.write( "short lines at those points:\r\n" );
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document.write( "   \r\n" );
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document.write( "Edwin
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