document.write( "Question 1033009: Find an equation of the ellipse that satisfies the given conditions:\r
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Algebra.Com's Answer #647681 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "Find an equation of the ellipse that satisfies the given conditions:\r
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document.write( "I assume that you are familiar with the material of the lesson  Ellipse definition, canonical equation, characteristic points and elements \r\n" );
document.write( "in this site. Surely, you may learn it from other sources. But if you are not familiar with it, I recommend you to read this lesson.\r\n" );
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document.write( "This ellipse has the center in the midpoint of the segment connecting the vertices. Obviously, the midpoint is the coordinate origin (0,0).\r\n" );
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document.write( "The major semi-axis has the length of 4 units.\r\n" );
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document.write( "So, the ellipse has a canonical equation of the form\r\n" );
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document.write( " +  = ,     (1)\r\n" );
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document.write( "where b is an unknown semi-minor axis.\r\n" );
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document.write( "We find b from the condition that the point (2,1) lies on the ellipse, so its coordinates satisfy the equation (1):\r\n" );
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document.write( " +  = .     (2)\r\n" );
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document.write( "Simplify it and solve for b:\r\n" );
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document.write( " =   --->   =   --->   =   --->   = .\r\n" );
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document.write( "Hence, b =  =  = .\r\n" );
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document.write( "Thus the minor semi-axis is b = , and the canonical equation of the ellipse is \r\n" );
document.write( " +  = .\r\n" );
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