document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=927550>Question 927550</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the hyperbola with the equation x^2&#8722;y^2&#8722;6x&#8722;2y+7=0, find the vertices, the foci, and the equations of the asymptotes. \r<BR>\n" );
document.write( "\n" );
document.write( "I can't seem to get the right answer, I get it to this equation(which is the standard equation but the denominators don't look right to me):\r<BR>\n" );
document.write( "\n" );
document.write( "(((x-3)^2)/1)-(((y-1)^2)/1)=1<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #563057 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=563057\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the hyperbola with the equation x^2&#8722;y^2&#8722;6x&#8722;2y+7=0, find the vertices, the foci, and the equations of the asymptotes. <BR>\n" );
document.write( "***<BR>\n" );
document.write( "x^2&#8722;6x&#8722;y^2&#8722;2y+7=0<BR>\n" );
document.write( "complete the square:<BR>\n" );
document.write( "(x^2&#8722;6x+9)&#8722;(y^2+2y+1)=-7+9-1<BR>\n" );
document.write( "(x-3)^2-(y+1)^2=1<BR>\n" );
document.write( "(x-3)^2/2-(y+1)^2/2=1<BR>\n" );
document.write( "This is an equation of a hyperbola with horizontal transverse axis.<BR>\n" );
document.write( "Its standard form of equation: <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)=coordinates of center.<BR>\n" );
document.write( "center:(3,-1)<BR>\n" );
document.write( "a^2=1<BR>\n" );
document.write( "a=1<BR>\n" );
document.write( "vertices:(3±a,-1)=(3±1,-1)=(4,-1) and (2,-1)<BR>\n" );
document.write( "b^2=1<BR>\n" );
document.write( "b=1<BR>\n" );
document.write( "c^2=a^2+b^2=1+1=2<BR>\n" );
document.write( "c=&#8730;2<BR>\n" );
document.write( "foci:(3±c,-1)=(3±&#8730;2,-1)=(3+&#8730;2,-1) and (3-&#8730;2,-1)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Asymptotes:Straight line equations of the form: y=mx+b, m=slope, b=y-intercept<BR>\n" );
document.write( "Asymptotes go thru center<BR>\n" );
document.write( "slope of asymptotes: ±b/a=±1<BR>\n" );
document.write( "..<BR>\n" );
document.write( "equation of asymptote with positive slope:<BR>\n" );
document.write( "y=x+b<BR>\n" );
document.write( "solve for b with coordinates of center<BR>\n" );
document.write( "-1=3+b<BR>\n" );
document.write( "b=-4<BR>\n" );
document.write( "equation: y=x-4<BR>\n" );
document.write( "..<BR>\n" );
document.write( "equation of asymptote with negative slope:<BR>\n" );
document.write( "y=-x+b<BR>\n" );
document.write( "solve for b with coordinates of center<BR>\n" );
document.write( "-1=-3+b<BR>\n" );
document.write( "b=2<BR>\n" );
document.write( "equation: y=-x+2 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );