document.write( "Question 1113290: find th eequation of ellipse having the given point as foci and the given number as the sum of the focal radi
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Algebra.Com's Answer #728305 by ikleyn(52786) $\"\"$ $\"About$

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document.write( "Let  \"a\"  and  \"b\"  be the major and minor semi-axes of the ellipse, respectively.\r\n" );
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document.write( "Then from the condition you have these two equations\r\n" );
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document.write( "(1)   (9+a) + (a-9) = 30             ( <<<---=== \"the sum of the focal radii = 30\" )\r\n" );
document.write( "                                     ( it is the sum of the distances from foci to the vertex of the ellipse !)\r\n" );
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document.write( "      which becomes  2a = 30  ====>  a = 15.\r\n" );
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document.write( "(2)    = 9            ( <<<---=== the distance from the center of the ellipse to its focus is 9).\r\n" );
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document.write( "      Then (2) implies   =  =  = 144,\r\n" );
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document.write( "      hence,  b =  = 12.\r\n" );
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document.write( "Thus the semi-axes are 15 and 12 units long,  and the equation of the ellipse is\r\n" );
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document.write( " +  = 1.\r\n" );
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