document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=455972>Question 455972</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have to find the center, vertices, co-vertices, foci, and asymptotes of the hyperbola <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x-y%5E2-4y-2=0 ALIGN=MIDDLE  ALT=\"x%5E2-2x-y%5E2-4y-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Can someone help me please? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #313108 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=313108\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I have to find the center, vertices, co-vertices, foci, and asymptotes of the hyperbola <BR>\n" );
document.write( "x^2-2x-y^2-4y-2=0<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Standard form of a hyperbola with horizontal transverse axis: (x-h)^2/a^2-(y-k)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "Standard form of a hyperbola with vertical transverse axis: (y-k)^2/a^2-(x-h)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "The difference between the two forms is the interchange of (x-h) and (y-k)<BR>\n" );
document.write( ".. <BR>\n" );
document.write( "x^2-2x-y^2-4y-2=0<BR>\n" );
document.write( "completing the square<BR>\n" );
document.write( "(x^2-2x+1)-(y^2+4y+4)=2+1+4=7<BR>\n" );
document.write( "(x-1)^2-(y+2)^2=7<BR>\n" );
document.write( "(x-1)^2/7-(y+2)^2/7=1<BR>\n" );
document.write( "This is a hyperbola with horizontal transverse axis (first form listed)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "center (1,-2)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "a^2=7<BR>\n" );
document.write( "a=&#8730;7<BR>\n" );
document.write( "vertices: (1±&#8730;7,-2)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b^2=7<BR>\n" );
document.write( "b=&#8730;7<BR>\n" );
document.write( "co-vertices:(1,-2±&#8730;7)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c^2=a^2+b^2=7+7=14<BR>\n" );
document.write( "c=&#8730;14<BR>\n" );
document.write( "foci: (1±&#8730;14,-2)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "asymptotes: <BR>\n" );
document.write( "slope=±b/a=±7/7=±1<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "using coordinates of center to find b since center is on asymptotes<BR>\n" );
document.write( "-2=±1+b<BR>\n" );
document.write( "b=-3 and -1<BR>\n" );
document.write( "equations of asymptotes<BR>\n" );
document.write( "y=x-3 (positive slope)<BR>\n" );
document.write( "y=-x-1 (negative slope)<BR>\n" );
document.write( "see graph below as a visual check on the answers above<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=((x-1)^2-7)^.5-2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%28%28x-1%29%5E2-7%29%5E.5-2%2C-%28%28x-1%29%5E2-7%29%5E.5-2%2Cx-3%2C-x-1%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );