document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=194672>Question 194672</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780395977255/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> i keep coming up with the wrong answers for the foci of this equation. please help.\r<BR>\n" );
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document.write( "4x^2-y^2+1=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #146057 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=146057\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "First, put it in standard form.  Either:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1\">\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1\">\r<BR>\n" );
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document.write( "If you add -1 to both sides you have something equal to -1 so you have to multiply the whole thing by -1, that gives you:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -4x^2 + y^2 = 1 \ \ \Rightarrow\ \ y^2 - 4x^2 = 1 \ \ \Rightarrow\ \ \frac{(y-0)^2}{1^2}-\frac{(x-0)^2}{\left({1 \over 2}\right)^2}=1\">\r<BR>\n" );
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document.write( "This hyperbola is centered at the origin and, because the y-term is the positive term, it opens up and down and the foci are on the y-axis at (0,c) where\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ c = \pm\sqrt{a^2 + b^2}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ c = \pm\sqrt{1 + {1 \over 4}} =\pm \frac{\sqrt{5}}{2}\">\r<BR>\n" );
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document.write( "Hence, the foci are at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(0,\frac{\sqrt{5}}{2}\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(0,-\frac{\sqrt{5}}{2}\right)\">\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" );
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