document.write( "Question 1071603: Find the equation of the hyperbola with center at (4,-1) transverse axis parallel to the y axis, distance between foci is 10 and latus rectum is 9/2 \n" ); document.write( "

Algebra.Com's Answer #686583 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "The green line above, drawn between foci, is given to \r\n" );
document.write( "be 10 units long.  The center is its midpoint, so the \r\n" );
document.write( "two foci are (4,4) and (4,-6).\r\n" );
document.write( "The two blue lines are the latus rectums. They are given\r\n" );
document.write( "as 9/2, so by subtraction of half that or 9/4 from\r\n" );
document.write( "the x-coordinate of the focus (4,4), we get that\r\n" );
document.write( "the left end of the upper latus rectum is the point\r\n" );
document.write( "(7/4,4).  The hyperbola goes through that point.\r\n" );
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document.write( "We know that the equation of the hyperbola is of the\r\n" );
document.write( "form\r\n" );
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document.write( "and since the center is (4,-1), it's\r\n" );
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document.write( "or\r\n" );
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document.write( "Since it goes through (7/4,4), we substitute that \r\n" );
document.write( "for (x,y) \r\n" );
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document.write( "We know that c = 5 because c is the distance from the\r\n" );
document.write( "center to the focus.\r\n" );
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document.write( "For all hyperbolas,  or ,\r\n" );
document.write( "and so \r\n" );
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document.write( "Substitute in\r\n" );
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document.write( ";  \r\n" );
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document.write( ";  \r\n" );
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document.write( "b� can only be positive, so\r\n" );
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document.write( "b� = 9 \r\n" );
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document.write( "Substitute in \r\n" );
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document.write( "So the equation:\r\n" );
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document.write( "becomes:\r\n" );
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document.write( "Edwin

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