document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091493>Question 1091493</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph each ellipse and clearly indicate the center, foci, vertices, and co-vertices<BR>\n" );
document.write( "x^2/16 - x/4 + y^2/9 + 4y/9 = 11/16\r<BR>\n" );
document.write( "\n" );
document.write( "PS This is on fractions!! 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 #705896 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=705896\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F16+-+x%2F4+%2B+y%5E2%2F9+%2B+4y%2F9+=+11%2F16 ALIGN=MIDDLE  ALT=\"x%5E2%2F16+-+x%2F4+%2B+y%5E2%2F9+%2B+4y%2F9+=+11%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > ..........complete squares\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F16%29%28x%5E2+-+4x%29%2B%281%2F9%29%28+y%5E2+%2B+4y%29+=+11%2F16 ALIGN=MIDDLE  ALT=\"%281%2F16%29%28x%5E2+-+4x%29%2B%281%2F9%29%28+y%5E2+%2B+4y%29+=+11%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F16%29%28x%5E2+-+4x%2Bb%5E2%29-%281%2F16%29b%5E2%2B%281%2F9%29%28+y%5E2+%2B+4y%2Bb%5E2%29-%281%2F9%29b%5E2+=+11%2F16+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F16%29%28x%5E2+-+4x%2B2%5E2%29-%281%2F16%292%5E2%2B%281%2F9%29%28+y%5E2+%2B+4y%2B2%5E2%29-%281%2F9%292%5E2+=+11%2F16+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F16%29%28x+-+2%29%5E2-%281%2F16%294%2B%281%2F9%29%28+y+%2B+2%29%5E2-%281%2F9%294+=+11%2F16+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F16%29%28x+-+2%29%5E2-%281%2F4%29%2B%281%2F9%29%28+y+%2B+2%29%5E2-%284%2F9%29=+11%2F16+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F16%29%28x+-+2%29%5E2%2B%281%2F9%29%28+y+%2B+2%29%5E2+=+11%2F16+%2B%281%2F4%29%2B%284%2F9%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F16%29%28x+-+2%29%5E2%2B%281%2F9%29%28+y+%2B+2%29%5E2+=+199%2F144 ALIGN=MIDDLE  ALT=\"%281%2F16%29%28x+-+2%29%5E2%2B%281%2F9%29%28+y+%2B+2%29%5E2+=+199%2F144\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2F16%29%2F%28199%2F144%29%29%28x+-+2%29%5E2%2B%28%281%2F9%29%2F%28199%2F144%29%29%28+y+%2B+2%29%5E2+=+%28199%2F144%29%2F%28199%2F144%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2F199%29%28x+-+2%29%5E2%2B%2816%2F199%29%28+y+%2B+2%29%5E2+=1 ALIGN=MIDDLE  ALT=\"%289%2F199%29%28x+-+2%29%5E2%2B%2816%2F199%29%28+y+%2B+2%29%5E2+=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+2%29%5E2%2F%28199%2F9%29%2B%28+y+%2B+2%29%5E2%2F%28199%2F16%29+=1 ALIGN=MIDDLE  ALT=\"%28x+-+2%29%5E2%2F%28199%2F9%29%2B%28+y+%2B+2%29%5E2%2F%28199%2F16%29+=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=2 ALIGN=MIDDLE  ALT=\"h=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-2 ALIGN=MIDDLE  ALT=\"k=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the center is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "\n" );
document.write( "semi-major axis length: \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=sqrt%28199%2F9%29+=sqrt%28199%29%2F3 ALIGN=MIDDLE  ALT=\"a=sqrt%28199%2F9%29+=sqrt%28199%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >&#8776; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4.7 ALIGN=MIDDLE  ALT=\"a=4.7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "semi-minor axis length:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b=sqrt%28199%2F16%29+=sqrt%28199%29%2F4 ALIGN=MIDDLE  ALT=\"+b=sqrt%28199%2F16%29+=sqrt%28199%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >&#8776;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3.5 ALIGN=MIDDLE  ALT=\"b=3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=a%5E2-b%5E2 ALIGN=MIDDLE  ALT=\"c%5E2=a%5E2-b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=199%2F9-199%2F16 ALIGN=MIDDLE  ALT=\"c%5E2=199%2F9-199%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=1393%2F144 ALIGN=MIDDLE  ALT=\"c%5E2=1393%2F144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%281393%2F144%29 ALIGN=MIDDLE  ALT=\"c=sqrt%281393%2F144%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%281393%29%2F12 ALIGN=MIDDLE  ALT=\"c=sqrt%281393%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "foci: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+-+c ALIGN=MIDDLE  ALT=\"h+-+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >) =(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+-+sqrt%281393%29%2F12 ALIGN=MIDDLE  ALT=\"2+-+sqrt%281393%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) &#8776; (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1.1 ALIGN=MIDDLE  ALT=\"-1.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) <BR>\n" );
document.write( "and<BR>\n" );
document.write( "foci :(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+%2Bc ALIGN=MIDDLE  ALT=\"h+%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >) =(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+%2Bsqrt%281393%29%2F12 ALIGN=MIDDLE  ALT=\"2+%2Bsqrt%281393%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2 ALIGN=MIDDLE  ALT=\"+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) &#8776; (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.1 ALIGN=MIDDLE  ALT=\"5.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2 ALIGN=MIDDLE  ALT=\"+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "\n" );
document.write( "vertices:\r<BR>\n" );
document.write( "\n" );
document.write( "The vertices are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+sqrt%28199%29%2F3 ALIGN=MIDDLE  ALT=\"a+=+sqrt%28199%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > units above and below the center, at <BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+-+sqrt%28199%29%2F3 ALIGN=MIDDLE  ALT=\"2+-+sqrt%28199%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) &#8776; (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2.7 ALIGN=MIDDLE  ALT=\"-2.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+%2B+sqrt%28199%29%2F3 ALIGN=MIDDLE  ALT=\"2+%2B+sqrt%28199%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) &#8776; (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.7 ALIGN=MIDDLE  ALT=\"6.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "\n" );
document.write( "The co-vertices are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+sqrt%28199%29%2F4 ALIGN=MIDDLE  ALT=\"b+=+sqrt%28199%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > units to either side of the center, at <BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Bsqrt%28199%29%2F4 ALIGN=MIDDLE  ALT=\"2%2Bsqrt%28199%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-sqrt%28199%29%2F4 ALIGN=MIDDLE  ALT=\"2-sqrt%28199%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );