document.write( "Question 1141350: Find an equation for the hyperbola with C(2,4), foci F1(2,1) and F2(2,7), and
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Algebra.Com's Answer #761900 by Edwin McCravy(20060) $\"\"$ $\"About$

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Find an equation for the hyperbola with C(2,4), foci F1(2,1) and F2(2,7), and
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document.write( "We plot those points:\r\n" );
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document.write( "It's a \"vertical\" hyperbola, opening up and down, like this: \r\n" );
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document.write( "so its equation is \r\n" );
document.write( "of the form:\r\n" );
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document.write( "The center (h,k) is C(2,4) so h=2 and k=4, so, substituting:\r\n" );
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document.write( "\"a\" is the distance from the center to the vertex.\r\n" );
document.write( "The distance from C(2,4) to V1(2,6) is 2 units and\r\n" );
document.write( "the distance from C(2,4) to V2(2,2) is also 2 units,\r\n" );
document.write( "so a=2.  So substituting:\r\n" );
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document.write( "\"c\" is the distance from the center to the focus.\r\n" );
document.write( "The distance from C(2,4) to F1(2,1) is 3 units and\r\n" );
document.write( "the distance from C(2,4) to F2(2,7) is also 3 units,\r\n" );
document.write( "so c=3.  So substituting:\r\n" );
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document.write( "We must calculate b using the Pythagorean relation for hyperbolas:\r\n" );
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document.write( "Substituting b²=5\r\n" );
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document.write( "Edwin

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