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document.write( "Write an equation for the hyperbola that satisfies\r\n" );
document.write( "each set of conditions. __ \r\n" );
document.write( "vertices (9,-3) and (-5,-3), foci at (2ｱﾖ53,-3)\r\n" );
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document.write( "This is a hyperbola that looks like this: }{\r\n" );
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document.write( "and has equation\r\n" );
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document.write( "(x-h)ｲ (y-k)ｲ \r\n" );
document.write( "覧覧覧 - 覧覧覧 = 1\r\n" );
document.write( " aｲ bｲ \r\n" );
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document.write( "where center = (h,k),\r\n" );
document.write( "a = semi-transverse axis, \r\n" );
document.write( "b = semi conjugate axis,\r\n" );
document.write( "foci (hｱc,k) where cｲ = aｲ+bｲ,\r\n" );
document.write( "and asaymptotes y - k = ｱ(b/a)(x - h)\r\n" );
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document.write( "The transverse axis is the line that goes from one vertex to the other.\r\n" );
document.write( "The distance between (9,-3) and (-5,-3) is 14 units.\r\n" );
document.write( "Therefore the semi-transverse axis, a = 7 units.\r\n" );
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document.write( "So far we have:\r\n" );
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document.write( "(x-h)ｲ (y-k)ｲ \r\n" );
document.write( "覧覧覧 - 覧覧覧 = 1\r\n" );
document.write( " 7ｲ bｲ \r\n" );
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document.write( "The center is midway between the foci, and since the midpoint between\r\n" );
document.write( "(9,-3) and (-5,-3) is (2,-3), that is the center (h,k)\r\n" );
document.write( "h = 2, k = -3\r\n" );
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document.write( "So far we have:\r\n" );
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document.write( "(x-2)ｲ (y+3)ｲ \r\n" );
document.write( "覧覧覧 - 覧覧覧 = 1\r\n" );
document.write( " 7ｲ bｲ \r\n" );
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document.write( "We only need b.\r\n" );
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document.write( "and we are given that (2ｱﾖ53,-3) are the foci.\r\n" );
document.write( "We know that the foci = (hｱc,k), or (2ｱc,-3), so\r\n" );
document.write( "c = ﾖ53\r\n" );
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document.write( "Also we know that\r\n" );
document.write( " __\r\n" );
document.write( "cｲ = aｲ+bｲ, and a = 7 and c = ﾖ53\r\n" );
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document.write( "(ﾖ53)ｲ = 7ｲ + bｲ\r\n" );
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document.write( " 53 = 49 + bｲ\r\n" );
document.write( " 4 = bｲ\r\n" );
document.write( " b = 2\r\n" );
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document.write( "So now we have b and the hyperbola is\r\n" );
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document.write( "(x-2)ｲ (y+3)ｲ \r\n" );
document.write( "覧覧覧 - 覧覧覧 = 1\r\n" );
document.write( " 7ｲ 2ｲ\r\n" );
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document.write( "or\r\n" );
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document.write( "(x-2)ｲ (y+3)ｲ \r\n" );
document.write( "覧覧覧 - 覧覧覧 = 1\r\n" );
document.write( " 49 4\r\n" );
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document.write( "
\r\n" );
document.write( " hyperbola only with asymptotes \r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com \n" );
document.write( "