document.write( "Question 927600: Find the equation for a hyperbola with eccentricity 3/2 and directrix x=2 \n" ); document.write( "

Algebra.Com's Answer #563156 by Edwin McCravy(20062) $\"\"$ $\"About$

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document.write( "The easiest hyperbola with directrix x=2 and eccentricity 3/2\r\n" );
document.write( "is found by taking the focus to be the origin.\r\n" );
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document.write( "We take an arbitrary point (x,y) on the hyperbola, and, (in blue)\r\n" );
document.write( "draw one line from the arbitrary point (x,y) to the focus (0,0) and\r\n" );
document.write( "another line directly to and perpendicular to the directrix x=2\r\n" );
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document.write( "The ratio of the two blue lines is equal to the eccentricity 3/2.\r\n" );
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document.write( "The horizontal blue line has length |2-x|,\r\n" );
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document.write( "The slanted blue line has length  or\r\n" );
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document.write( "So we set their ratio equal to 3/2\r\n" );
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document.write( "Square both sides\r\n" );
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document.write( "Edwin

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