document.write( "Question 284081: what is the equation for the conic section? it is an ellipse with the vertices
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Algebra.Com's Answer #206373 by Edwin McCravy(20060)\"\" \"About 
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what is the equation for the conic section? it is an ellipse with the vertices
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document.write( "what is the equation for the conic section? it is an ellipse with the vertices\r\n" );
document.write( "(-2,4) and (-2,-6). covertices are (-4,-1) and (0,-1). and what are the foci? \r\n" );
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document.write( "Plot those 4 points:\r\n" );
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document.write( "Connect them to show the major and minor axes\r\n" );
document.write( "of the ellipse:\r\n" );
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document.write( "Sketch in the ellipse:\r\n" );
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document.write( "Since the ellipse has its major axis vertical,\r\n" );
document.write( "it has the standard form:\r\n" );
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document.write( "\"%28x-h%29%5E2%2Fb%5E2+%2B+%28y-k%29%5E2%2Fa%5E2+=+1\"\r\n" );
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document.write( "where \r\n" );
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document.write( "1. (h,k) = the center \r\n" );
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document.write( "2. a = the distance from the center to either of the two vertices\r\n" );
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document.write( "3. b = the distance from the center to either of the the covertices.\r\n" );
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document.write( "We can see from the graph that \r\n" );
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document.write( "1. the center of the ellipse is (h,k) = (-2,-1)\r\n" );
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document.write( "2. a = 5\r\n" );
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document.write( "3. b = 2\r\n" );
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document.write( "So the equation \r\n" );
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document.write( "\"%28x-h%29%5E2%2Fb%5E2+%2B+%28y-k%29%5E2%2Fa%5E2+=+1\"\r\n" );
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document.write( "becomes\r\n" );
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document.write( "\"%28x-%28-2%29%29%5E2%2F2%5E2+%2B+%28y-%28-1%29%29%5E2%2F5%5E2+=+1\"\r\n" );
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document.write( "or\r\n" );
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document.write( "\"%28x%2B2%29%5E2%2F4+%2B+%28y%2B1%29%5E2%2F25+=+1\"\r\n" );
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document.write( "to find the foci, we calculate c by\r\n" );
document.write( "this Pythagorean relation:\r\n" );
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document.write( "\"c%5E2=a%5E2-b%5E2\"\r\n" );
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document.write( "\"c%5E2=5%5E2-2%5E2\"\r\n" );
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document.write( "\"c%5E2=25-4\"\r\n" );
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document.write( "\"c%5E2=21\"\r\n" );
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document.write( "\"c=sqrt%2821%29\"\r\n" );
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document.write( "The two foci are on the major axis c usits\r\n" );
document.write( "from the center, so they are\r\n" );
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document.write( "(-2,-1+\"sqrt%2821%29\") and (-2,-1-\"sqrt%2821%29\")\r\n" );
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document.write( "Edwin
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