document.write( "Question 1185036: Can you help me with these? Please
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Algebra.Com's Answer #815755 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We plot those given points and sketch in a rough sketch of the\r\n" );
document.write( "hyperbola.  All \"conic\" graphs curve around their focal points.\r\n" );
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document.write( "The equation of all hyperbolas that open right and left have equations,\r\n" );
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document.write( "\"%28x-h%29%5E2%2Fa%5E2\"\"%22%22-%22%22\"\"%28y-k%29%5E2%2Fb%5E2\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( "where (h,k) is the center, \"a\" is the distance between the center and\r\n" );
document.write( "either vertex. \"c\" is the distance between the center and either focal\r\n" );
document.write( "point (or focus).  But \"c\" does not appear in the standard equation of\r\n" );
document.write( "a hyperbola. We calculate \"b2\" by the Pythagorean theorem:\r\n" );
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document.write( "\"c%5E2=a%5E2%2Bb%5E2\"\r\n" );
document.write( "\"5%5E2=4%5E2%2Bb%5E2\"\r\n" );
document.write( "\"25=16%2Bb%5E2\"\r\n" );
document.write( "\"9=b%5E2\"\r\n" );
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document.write( "The center is (0,0), so h=0, k=0, a2=4^2=16, b2=3^2=9.\r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "\"%28x-h%29%5E2%2Fa%5E2\"\"%22%22-%22%22\"\"%28y-k%29%5E2%2Fb%5E2\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( "\"%28x-0%29%5E2%2F16%5E%22%22\"\"%22%22-%22%22\"\"%28y-0%29%5E2%2F9%5E%22%22\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( "\"x%5E2%2F16%5E%22%22\"\"%22%22-%22%22\"\"y%5E2%2F9%5E%22%22\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( "Edwin
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