document.write( "Question 1206860: Find the equation of the hyperbola with vertices at (-4,2)
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Algebra.Com's Answer #844549 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "The vertices and foci lie on the horizontal line y=2, since all their y-coordinates have y-coordinate 2.\r\n" );
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document.write( "It looks like this:\r\n" );
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document.write( "Therefore the hyperbola has the equation\r\n" );
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document.write( "where the vertex is the midpoint between vertices, and also the midpoint\r\n" );
document.write( "between foci. That is, the vertex is (-2,2).\r\n" );
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document.write( "a = semi-transverse axis = distance from center to vertex = 2 units\r\n" );
document.write( "c = semi-conjugate axis = half the height of defining rectangle = \r\n" );
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document.write( "Find the equation of the hyperbola with vertices at (-4,2) \r\n" );
document.write( "and (0,2) and foci at (-5,2) and (1,2).\r\n" );
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document.write( "So we have the center, so we can determine everything about the equation\r\n" );
document.write( "except b.\r\n" );
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document.write( "(h,k) the center = (-2,2), a=2\r\n" );
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document.write( "We use the Pythagorean relation for hyperbolas to find b:\r\n" );
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document.write( "  <-- what we need for the denominator:\r\n" );
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document.write( "  <--answer\r\n" );
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document.write( "The defining rectangle is in green.\r\n" );
document.write( "The blue line is the transverse axis, 2a or 4 in length\r\n" );
document.write( "The red line is the conjugate axis 2b or  in length.\r\n" );
document.write( "The gold lines are the asymptotes of the hyperbola, the extended diagonals\r\n" );
document.write( "of the defining rectangle.\r\n" );
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document.write( "Edwin

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