document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=706005>Question 706005</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how can i find the focus/foci and vertex/vertices\r<BR>\n" );
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document.write( "x^2-4y^2-2x+16y=20\r<BR>\n" );
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document.write( "this is how far i have gotten, but i am not sure if it is right so far\r<BR>\n" );
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document.write( "x^2-4y^2-2x+16y=20<BR>\n" );
document.write( "(x^2-2x+1)-4(y^2+4y+4)=20+1+4<BR>\n" );
document.write( "(x-1)^2/25-4(y+4)^2/25=25/25<BR>\n" );
document.write( "(x-1)^2/25-4(y+4)^2/25=1\r<BR>\n" );
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document.write( "please help. thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #434916 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=434916\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (x^2\ -\ 2x\ +\ 1)\ -\ 4(y^2\ -\ 4y\ +\ 4)\ =\ 20\ +\ 1\ -\ 16\">\r<BR>\n" );
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document.write( "Note the -4 coefficient OUTSIDE the parentheses so the 1st degree y term has to have a coefficient of -4 (-4 times -4 is +16), then in order to complete the square inside the parentheses you need a +4, and +4 times -4 is -16.  What you add to the left must be added to the right, hence the -16 in the RHS.\r<BR>\n" );
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document.write( "From there:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{(x\ -\ 1)^2}{5}\ -\ \frac{4(y\ -\ 2)^2}{5}\ =\ 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{(x\ -\ 1)^2}{5}\ -\ \frac{(y\ -\ 2)^2}{\frac{5}{4}}\ =\ 1\">\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a\ =\ sqrt{5}\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE b\ =\ \frac{\sqrt{5}}{2}\">\r<BR>\n" );
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document.write( "Can you take it from there?\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( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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