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 #434927 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=434927\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> how can i find the focus/foci and vertex/vertices <BR>\n" );
document.write( "x^2-4y^2-2x+16y=20<BR>\n" );
document.write( "complete the square:<BR>\n" );
document.write( "x^2-2x-4y^2+16y=20<BR>\n" );
document.write( "(x^2-2x+1)-4(y^2-4y+4)=20+1-16<BR>\n" );
document.write( "(x-1)^2-4(y-2)^2=5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2%2F5-4%28y-2%29%5E2%2F%285%2F4%29=1 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2%2F5-4%28y-2%29%5E2%2F%285%2F4%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is an equation of a hyperbola with horizontal transverse axis.<BR>\n" );
document.write( "Its standard form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, (h,k)=(x,y) coordinates of the center.<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "Center: (1,2)<BR>\n" );
document.write( "a=5<BR>\n" );
document.write( "a^2=25<BR>\n" );
document.write( "vertices: (1±a,2)=(1±5,2)=(-4,2) and (6,2)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b=5/4<BR>\n" );
document.write( "b^2=25/16<BR>\n" );
document.write( "..<BR>\n" );
document.write( "foci<BR>\n" );
document.write( "c^2=a^2+b^2=25+(25/16)=425/16<BR>\n" );
document.write( "c=&#8730;425/4&#8776;5.15<BR>\n" );
document.write( "foci:(1±c,2)=(1±5.15,2)=(-4.15,2) and (6.15,2)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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