document.write( "Question 1186658: An ellipse has vertices (2 − √ 61, 5) and (2 + √ 61, 5), and its minor axis is 12 units long. Find its standard equation and its foci.
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Algebra.Com's Answer #817622 by ikleyn(52802) $\"\"$ $\"About$

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\n" ); document.write( "An ellipse has vertices (2 − √ 61, 5) and (2 + √ 61, 5), and its minor axis is 12 units long.
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\n" ); document.write( "\n" ); document.write( " It can be done (and it should be done) in much shorter way, than @MathLover1 does it.\r
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\n" ); document.write( "\n" ); document.write( " It does not require so intensive calculations.\r
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document.write( "Looking at the foci coordinates, you see that they are on the horizontal line y = 5.\r\n" );
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document.write( "So, the major axis is horizontal, parallel to x-axis, and the length of the horizontal axis is  \r\n" );
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document.write( "      -  = .\r\n" );
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document.write( "Hence, the length of the major semi-axis  \"a\"  is half of it, i.e.  a = .\r\n" );
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document.write( "The length of the minor semi-axis is  b =  = 6.\r\n" );
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document.write( "The center of the ellipse is the point (2,5).\r\n" );
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document.write( "THEREFORE, the standard form equation of the ellipse is\r\n" );
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document.write( "     +  = 1.    ANSWER\r\n" );
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document.write( "The distance from the center to the focus is  c =  =  =  = 5.\r\n" );
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document.write( "The foci are  (2+5,5) = (7,5)  and  (2-5,5) = (-3,5).\r\n" );
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