document.write( "Question 480300: find the ellipse in standard form that passes through the
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Algebra.Com's Answer #328968 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
point(3,\"sqrt%287%29\") and (\"sqrt%283%29\",3)?
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document.write( "Here are those two points plotted: approximately (3,2.6) and (1.7,3)\r\n" );
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document.write( "I will assume you meant the ellipse with center at the origin; \r\n" );
document.write( "otherwise there would be many possibilities.\r\n" );
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document.write( "Since those points are as they are, the major axis will be\r\n" );
document.write( "horizontal and the ellipse will look like this:  ᆼ\r\n" );
document.write( "So its equation will be:\r\n" );
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document.write( "\"x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2=1\"\r\n" );
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document.write( "Substitute the first point: (x, y) = (3, \"sqrt%287%29\")\r\n" );
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document.write( "\"%283%29%5E2%2Fa%5E2%2B%28sqrt%287%29%29%5E2%2Fb%5E2=1\"\r\n" );
document.write( "\"9%2Fa%5E2%2B7%2Fb%5E2=1\"\r\n" );
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document.write( "Substitute the second point: (x, y) = (\"sqrt%283%29\",3)?\r\n" );
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document.write( "\"%28sqrt%283%29%29%5E2%2Fa%5E2%2B%283%29%5E2%2Fb%5E2=1\"\r\n" );
document.write( "\"3%2Fa%5E2%2B9%2Fb%5E2=1\"\r\n" );
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document.write( "We have this system of equations:\r\n" );
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document.write( "\"system%289%2Fa%5E2%2B7%2Fb%5E2=1%2C3%2Fa%5E2%2B9%2Fb%5E2=1%29\"\r\n" );
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document.write( "Important!:\r\n" );
document.write( "DO NOT CLEAR OF FRACTIONS BUT SOLVE BY ELIMINATION:\r\n" );
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document.write( "Multiply the 2nd equation through by -3 to eliminate the\r\n" );
document.write( "terms in aČ:\r\n" );
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document.write( "\"system%289%2Fa%5E2%2B7%2Fb%5E2=1%2C-9%2Fa%5E2-27%2Fb%5E2=-3%29\"\r\n" );
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document.write( "Add the equations:\r\n" );
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document.write( "\"-20%2Fb%5E2=-2\"\r\n" );
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document.write( "\"-20=-2b%5E2\"\r\n" );
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document.write( "\"10=b%5E2\"\r\n" );
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document.write( "Substitute 10 for bČ in the first equation:\r\n" );
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document.write( "\"9%2Fa%5E2%2B7%2Fb%5E2=1\"\r\n" );
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document.write( "\"9%2Fa%5E2%2B7%2F10=1\"\r\n" );
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document.write( "Multiply through by 10aČ\r\n" );
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document.write( "\"90%2B7a%5E2=10a%5E2\"\r\n" );
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document.write( "\"90=3a%5E2\"\r\n" );
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document.write( "\"30=a%5E2\"\r\n" );
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document.write( "Substitute 30 for aČ and 10 for bČ\r\n" );
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document.write( "\"x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2=1\"\r\n" );
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document.write( "\"x%5E2%2F30%2By%5E2%2F10=1\"\r\n" );
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document.write( "That's the equation.  \r\n" );
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document.write( "The vertices are (±\"sqrt%2830%29\",0), approximately (±5.5,0)\r\n" );
document.write( "The covertices are (0,±\"sqrt%2810%29\"), approximately (0,±3.2)\r\n" );
document.write( "Here's the graph:\r\n" );
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document.write( "Edwin
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