document.write( "Question 608548: Write the equation in standard form for the conic section.\r
\n" ); document.write( "\n" ); document.write( "An ellipse centered at (3,2) with vertices at (9,2) and (-3,2)and co vertices at (3,5) and (3,-1) \n" ); document.write( "

Algebra.Com's Answer #383294 by Edwin McCravy(20060) $\"\"$ $\"About$

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Write the equation in standard form for the conic section.
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document.write( "I think you need a more graphical approach than just a word explanation.\r\n" );
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document.write( "Plot the points and draw the graph:\r\n" );
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document.write( "Since the ellipse is this way \"\" and not this way \"\", its equation is:\r\n" );
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document.write( "    +  = 1\r\n" );
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document.write( "[Had it been the other way the \"a\" and \"b\" would be switched. In an\r\n" );
document.write( "ellipse \"a\" is always larger than \"b\", but not necessarily in a hyperbola!]\r\n" );
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document.write( "(h,k) = the center = (3,2),  \"a\" = semi-major-axis, sometimes called\r\n" );
document.write( "\"the long radius\" and \"b\" = the semi-minor-axis, sometimes called\r\n" );
document.write( "\"the short radius\".\r\n" );
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document.write( "draw the semi-major and semi-minor axes:\r\n" );
document.write( "The red line is the semi-major axis and the green line is the semi-minor\r\n" );
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document.write( "Count the number of units that the red and green lines are in\r\n" );
document.write( "length and you'll get a = 6 and b = 3.  Therefore the equation\r\n" );
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document.write( " +  = 1\r\n" );
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document.write( "becomes:\r\n" );
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document.write( " +  = 1\r\n" );
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document.write( "or\r\n" );
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document.write( " +  = 1\r\n" );
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document.write( "Edwin

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