document.write( "Question 1186200: Find the standard form of the equation of the ellipse with the given characteristics.
\n" ); document.write( "Center: (3, −8); a = 8c; foci: (3, −9), (3, −7)\r
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Algebra.Com's Answer #817085 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Find the standard form of the equation of the ellipse with the given characteristics.
\n" ); document.write( "Center: (3, −8); a = 8c; foci: (3, −9), (3, −7)
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document.write( "Notice that the foci lie on vertical line x = 3.\r\n" );
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document.write( "It means that the major axis of the ellipse is vertical  x= 3, parallel to y-axis,\r\n" );
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document.write( "and the minor axis is horizontal y= -8, parallel to x-axis.\r\n" );
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document.write( "The distance between the foci is  2c = -7 - (-9) = 2;  hence, the linear eccentricity is half of this distance c = 2/2 = 1.\r\n" );
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document.write( "Further, the major semi-axis  a = 8c = 8;  hence, the minor semi-axis is  b =  =  = .\r\n" );
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document.write( "Now we are ready to write the standard form equation of the ellipse\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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