document.write( "Question 971243: Can you help me to my question please? :(\r
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Algebra.Com's Answer #593791 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
General Equation of Hyperbola
\n" ); document.write( "with vertices (2,-1) and (2,-5) ; the Latus Rectum is 12
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document.write( "We plot the two vertices and the center which is the midpoint\r\n" );
document.write( "between them (2,-3), and sketch the hyperbola approximately, which must \r\n" );
document.write( "open up and down.\r\n" );
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document.write( "Since the hyperbola opens upward and downward, it has the equation:\r\n" );
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document.write( "\"%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1\"\r\n" );
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document.write( "The center is (h,k) = (2,-3), the midpoint between vertices, and \r\n" );
document.write( "a = 2, the distance between the center and a vertex.\r\n" );
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document.write( "So we have everything but b\r\n" );
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document.write( "\"%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1\"\r\n" );
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document.write( "\"%28y-%28-3%29%29%5E2%2F2%5E2-%28x-2%29%5E2%2Fb%5E2=1\"\r\n" );
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document.write( "\"%28y%2B3%29%5E2%2F4-%28x-2%29%5E2%2Fb%5E2=1\"\r\n" );
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document.write( "If you have studied the formula for the length of the\r\n" );
document.write( "latus rectum which is \"2b%5E2%2Fa\", we can use that to \r\n" );
document.write( "find b:\r\n" );
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document.write( "\"2b%5E2%2Fa=12\"\r\n" );
document.write( "\"2b%5E2%2F2=12\"\r\n" );
document.write( "\"b%5E2=12\"\r\n" );
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document.write( "we have the equation\r\n" );
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document.write( "\"%28y%2B3%29%5E2%2F4-%28x-2%29%5E2%2Fb%5E2=1\"\r\n" );
document.write( "\"%28y%2B3%29%5E2%2F4-%28x-2%29%5E2%2F12=1\"\r\n" );
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document.write( "That's the standard equation.  The general equation can be \r\n" );
document.write( "gotten by multiplying through by LCD=12, squaring the\r\n" );
document.write( "binomials and simplifying: \r\n" );
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document.write( "\"x%5E2-3y%5E2-4x-18y-11=0\"\r\n" );
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document.write( "There is another way to get this answer if you haven't\r\n" );
document.write( "studied the latus rectum formula.  Let me know in the \r\n" );
document.write( "thank-you note form below if you haven't studied that \r\n" );
document.write( "formula, and I'll show you how to find b without using \r\n" );
document.write( "it.\r\n" );
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document.write( "Edwin
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