document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=948467>Question 948467</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Locate the center, foci, vertices, ends of latera recta, & draw the ellipse. also compute the eccentricity & find the equation of the directices. \r<BR>\n" );
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document.write( "2.x^2/36+y^2/16=1<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #579644 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=579644\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F36%2By%5E2%2F16=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F36%2By%5E2%2F16=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "STANDARD FORM:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2F%28a%5E2%29%2B%28y-k%29%5E2%2F%28b%5E2%29=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2F%28a%5E2%29%2B%28y-k%29%5E2%2F%28b%5E2%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "CENTER: Center is at (h,k) in this case (0,0). Center is at origin.\r<BR>\n" );
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document.write( "FOCI: Focus is (f) from center <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E2=a%5E2-b%5E2 ALIGN=MIDDLE  ALT=\"f%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=f%5E2=36-16=20 ALIGN=MIDDLE  ALT=\"f%5E2=36-16=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Find square root of each side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=sqrt%2820%29 ALIGN=MIDDLE  ALT=\"f=sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " Foci are at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%2820%29 ALIGN=MIDDLE  ALT=\"-sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%29 ALIGN=MIDDLE  ALT=\"sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >). \r<BR>\n" );
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document.write( "VERTICES: In this case at (+ or - a,0) and a=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836%29 ALIGN=MIDDLE  ALT=\"sqrt%2836%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=6<BR>\n" );
document.write( "  Vertices at (-6,0) and (6,0)\r<BR>\n" );
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document.write( "ENDPOINTS OF LATERA RECTA: The latera recta are perpendicular to the major axis at the foci, and have length: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2%2Fa ALIGN=MIDDLE  ALT=\"2b%5E2%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since half is above and half is below the axis, we need half the length or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2Fa ALIGN=MIDDLE  ALT=\"b%5E2%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >=16/6=8/3<BR>\n" );
document.write( "For the focus at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%2820%29 ALIGN=MIDDLE  ALT=\"-sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >),<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >), the endpoints of the latus rectum are  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%2820%29 ALIGN=MIDDLE  ALT=\"-sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2F3%29 ALIGN=MIDDLE  ALT=\"%288%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%2820%29 ALIGN=MIDDLE  ALT=\"-sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%288%2F3%29 ALIGN=MIDDLE  ALT=\"-%288%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "For the focus at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%29 ALIGN=MIDDLE  ALT=\"sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >), the endpoints of the latus rectum are (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%29 ALIGN=MIDDLE  ALT=\"sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2F3%29 ALIGN=MIDDLE  ALT=\"%288%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%29 ALIGN=MIDDLE  ALT=\"sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%288%2F3%29 ALIGN=MIDDLE  ALT=\"-%288%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "ECCENTRICITY: Eccentricity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=epsilon ALIGN=MIDDLE  ALT=\"epsilon\"   DISABLED_style= \"max-width:90%; height:auto;\" >=f/a=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%29%2F6 ALIGN=MIDDLE  ALT=\"sqrt%2820%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "EQUATIONS OF DIRECTRICES: directrix is a line perpendicular to the main axis<BR>\n" );
document.write( "on opposite the vertex from the focus, and same distance as the focus from the vertex. The directrix is outside the ellipse. The  is a+(a-f) from the center,<BR>\n" );
document.write( "or in this case, the directrix to the right of the origin is x=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2B%286-sqrt%2820%29%29 ALIGN=MIDDLE  ALT=\"6%2B%286-sqrt%2820%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12-sqrt%2820%29 ALIGN=MIDDLE  ALT=\"12-sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and to the left of the origin x=-(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12-sqrt%2820%29 ALIGN=MIDDLE  ALT=\"12-sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >).  \r<BR>\n" );
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