document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=629704>Question 629704</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the correct vertices, foci, and asymptotes for the following hyperbola?:\r<BR>\n" );
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document.write( "x^2-y^2+2x+6y-9=0\r<BR>\n" );
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document.write( "I completed the squares and ended up with this:<BR>\n" );
document.write( "(x+1)^2/(19) - (y-3)^2/(19)=1\r<BR>\n" );
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document.write( "But when I plug in (h-a,k)(h+a,k) the answer is not correct for the vertices:<BR>\n" );
document.write( "(-1-&#8730;19)(-1+&#8730;19)\r<BR>\n" );
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document.write( "or \r<BR>\n" );
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document.write( "(-1-&#8730;38,3)(-1+&#8730;38,3)for the foci.\r<BR>\n" );
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document.write( "What am I doing wrong?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #396453 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=396453\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\" color = \"black\">\r<BR>\n" );
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document.write( "Keeping the signs straight when completing the square on the general quadratic for a hyperbola can be a little tricky.  Watch carefully:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ y^2\ +\ 2x\ +\ 6y\ -\ 9\ =\ 0\">\r<BR>\n" );
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document.write( "Move the constant term to the RHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ y^2\ +\ 2x\ +\ 6y\ =\ 9\">\r<BR>\n" );
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document.write( "Rearrange:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 2x\ -\ y^2\ +\ 6y\ =\ 9\">\r<BR>\n" );
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document.write( "Since you are working a hyperbola, group the \"negative variable\" terms with parentheses:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 2x\ -\ (y^2\ -\ 6y\ )\ =\ 9\">\r<BR>\n" );
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document.write( "Note the sign change on the first degree <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> term because of the distributive law.\r<BR>\n" );
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document.write( "Now complete the square on both variables:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 2x\ +\ 1\ -\ (y^2\ -\ 6y\ +\ 9)\ =\ 9\ +\ 1\ -\ 9\">\r<BR>\n" );
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document.write( "Notice that because you are adding a +9 INSIDE of the parentheses on the left, you are actually adding a -9 to the LHS.  So you need a -9 in the RHS to make up for it.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x\ +\ 1)^2\ -\ (y\ -\ 3)^2\ =\ 1\">.\r<BR>\n" );
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document.write( "so center at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (-1, 3)\"> just like you had it, but <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a\ =\ 1\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE b\ =\ 1\">, and therefore <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE c\ =\ \sqrt{2}\">\r<BR>\n" );
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document.write( "I think you can take it from here, can you not?\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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