document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=411504>Question 411504</A>: <I><SPAN STYLE=\"word-break: break-all;\"> analyze the equation x^2+9y^2+6x-18y+9=0; that is find the center,foci,vertices, and graph<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 #289248 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=289248\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> analyze the equation x^2+9y^2+6x-18y+9=0; that is find the center,foci,vertices, and graph<BR>\n" );
document.write( "..\r<BR>\n" );
document.write( "\n" );
document.write( "completing the squares,<BR>\n" );
document.write( "(x^2+6x+9)+9(y^2-2y+1)=-9+9+9=9<BR>\n" );
document.write( "(x+3)^2+9(y-1)^2=9<BR>\n" );
document.write( "(x+3)^2/9+(y-1)^2/1=1<BR>\n" );
document.write( "This equation is a standard form of an ellipse:(x-h)^2/a^2+(y-k)^2/b^2=1<BR>\n" );
document.write( "Major axis is horizontal and center at (-3,1)<BR>\n" );
document.write( "a^2=9<BR>\n" );
document.write( "a=3<BR>\n" );
document.write( "b^1=1<BR>\n" );
document.write( "b=1<BR>\n" );
document.write( "c=sqrt(a^2-b^2)=sqrt(8)=2.83<BR>\n" );
document.write( "vertices: (-6,1) and 0,1)<BR>\n" );
document.write( "foci: (4.83,1),(.83,1)<BR>\n" );
document.write( "see graph below<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=1+((9-(x+3)^2)/9)^.5\r<BR>\n" );
document.write( "\n" );
document.write( "..\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-8%2C+3%2C+-5%2C+5%2C+1%2B%28%289-%28x%2B3%29%5E2%29%2F9%29%5E.5%2C1-%28%289-%28x%2B3%29%5E2%29%2F9%29%5E.5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );