document.write( "Question 1096051: for the ellipse x^2/a^2 + y^2/b^2=1 with foci at (-c,0) and (c,0), show that b^2 = a^2 – c^2 \n" ); document.write( "

Algebra.Com's Answer #710550 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "The definition of an ellipse is:\r\n" );
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document.write( "An ellipse is a curved line forming a closed loop, where the sum \r\n" );
document.write( "of the distances from two points (foci) to every point on the line \r\n" );
document.write( "is constant.\r\n" );
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document.write( "Therefore since (0,b), and (a,0) are points on the ellipse,\r\n" );
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document.write( "the sum of the distances indicated by the two red lines must be equal\r\n" );
document.write( "to the constant, and also the sum of the two straight distances \r\n" );
document.write( "indicated by the two green curved lines must also equal the the same\r\n" );
document.write( "constant. \r\n" );
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document.write( "Since a > c > 0, then, \r\n" );
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document.write( "Edwin

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