document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=949013>Question 949013</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Identify the center, vertices, co-vertices, foci, length of the major axis, length of the minor axis, and eccentricity of:<BR>\n" );
document.write( "X squared + 9y squared + 8x + 108y +331= 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #579298 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=579298\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Identify the center, vertices, co-vertices, foci, length of the major axis, length of the minor axis, and eccentricity of:<BR>\n" );
document.write( "X squared + 9y squared + 8x + 108y +331= 0<BR>\n" );
document.write( "***<BR>\n" );
document.write( "x^2+9y^2+8x+108y+331=0<BR>\n" );
document.write( "x^2+8x+9y^2+108y=-331<BR>\n" );
document.write( "complete the square:<BR>\n" );
document.write( "(x^2+8x+16)+9(y^2+12y+36)=-331+16+324<BR>\n" );
document.write( "(x+4)^2+9(y+6)^2=9<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E2%2F9%2B%28y%2B6%29%5E2=1 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2%2F9%2B%28y%2B6%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is an equation of an ellipse with horizontal major 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%2B%28y-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"+%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a>b, (h,k)=coordinates of center<BR>\n" );
document.write( "center: (-4,-6)<BR>\n" );
document.write( "a^2=9<BR>\n" );
document.write( "a=&#8730;9=3<BR>\n" );
document.write( "length of major axis=2a=6<BR>\n" );
document.write( "b^2=1<BR>\n" );
document.write( "b=1<BR>\n" );
document.write( "length of minor axis=2b=2<BR>\n" );
document.write( "vertices: (-4±a,-6)=(-4±3,-6)=(-7,-6) and (-1,-6)<BR>\n" );
document.write( "co-vertices: (-4-6±b)=(-4,-6±1)=(-4,-7) and (-4,-5)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c^2=a^2-b^2=9-1=8<BR>\n" );
document.write( "c=&#8730;8&#8776;2.8<BR>\n" );
document.write( "foci: (-4±c,-6)=(-4±2.8,-6)=(-6.8,-6) and (-1.2,-6)<BR>\n" );
document.write( "eccentricity=c/a=&#8730;8/3&#8776;0.94<BR>\n" );
document.write( "see graph below:<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%289-%28x%2B4%29%5E2%29%2F9%29%5E.5-6%2C-%28%289-%28x%2B4%29%5E2%29%2F9%29%5E.5-6%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );