document.write( "Question 407139: What is the equation for a hyperbola with vertices of (0, 7) and (0, -7), and a conjugate axis with the length of 18 units? \n" ); document.write( "

Algebra.Com's Answer #287047 by Edwin McCravy(20056) $\"\"$ $\"About$

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What is the equation for a hyperbola with vertices of (0, 7) and (0, -7), and a conjugate axis with the length of 18 units?
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document.write( "We plot the vertices:\r\n" );
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document.write( "So we can see that the center is (h,k) = (0,0) and that the hyperbola\r\n" );
document.write( "must open upward and downward, so the equation is of the form\r\n" );
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document.write( "The transverse axis joins the vertices, so we draw it in green\r\n" );
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document.write( "So \"a\" is the length of the semi-transverse axis or the distance \r\n" );
document.write( "from the center to either vertex, and we see that a = 7\r\n" );
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document.write( "The conjugate axis and the transverse axis bisect each other at\r\n" );
document.write( "the center, and we are given that the conjugate axis is 18 units,\r\n" );
document.write( "so we draw it also in green with its midpoint at the center:\r\n" );
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document.write( "Since \"b\" is the length of the semi-conjugate axis we see that b = 9,\r\n" );
document.write( "half the given length of the conjugaste axis.\r\n" );
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document.write( "Next we draw the defining rectangle with the ends of the \r\n" );
document.write( "transverse and conjugate axes bisecting the sides:\r\n" );
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document.write( "Then we draw the extended diagonals of the defining rectangle,\r\n" );
document.write( "which are the asymptotes of the hyperbola:\r\n" );
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document.write( "Now we can easily sketch in the hyperbola:\r\n" );
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document.write( "And the equation \r\n" );
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document.write( "becomes\r\n" );
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document.write( "or\r\n" );
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document.write( "Edwin

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