document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=692119>Question 692119</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me figure out how to graph this ellipse:\r<BR>\n" );
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document.write( "(4/9)x^2 + 81y^2 = 1\r<BR>\n" );
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document.write( "I am unsure of what the fist step in this should be.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #427005 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=427005\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  figure out how to graph this ellipse: <BR>\n" );
document.write( "(4/9)x^2 + 81y^2 = 1<BR>\n" );
document.write( "standard form of equation for an ellipse with horizontal major axis: <BR>\n" );
document.write( "<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)=(x,y) coordinates of center.<BR>\n" );
document.write( "...<BR>\n" );
document.write( "standard form of equation for an ellipse with vertical major axis: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a>b, (h,k)=(x,y) coordinates of center.<BR>\n" );
document.write( "note: a and b interchanged<BR>\n" );
document.write( "...<BR>\n" );
document.write( "To graph given ellipse:<BR>\n" );
document.write( "The first step is to write the equation in standard form for an ellipse<BR>\n" );
document.write( "(4/9)x^2 + 81y^2 =1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F%289%2F4%29%2By%5E2%2F%281%2F81%29=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F%289%2F4%29%2By%5E2%2F%281%2F81%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "note the absence of h and k, so center is at (0,0)<BR>\n" );
document.write( "a^2=9/4<BR>\n" );
document.write( "b^2=1/81<BR>\n" );
document.write( "a>b, so ellipse has a horizontal major axis<BR>\n" );
document.write( "...<BR>\n" );
document.write( "a^2=9/4<BR>\n" );
document.write( "a=&#8730;(9/4)=3/2<BR>\n" );
document.write( "vertices: (0±a,0)=(0±3/2,0)=(-3/2,0) and (3/2,0) (end points of horizontal major axis or x intercepts)<BR>\n" );
document.write( "b^2=1/81<BR>\n" );
document.write( "b=&#8730;(1/81)=1/9<BR>\n" );
document.write( "co-vertices: (0,0±b)=(0,0±1/9)=(0,-1/9) and (0,1/9) (end points of minor axis or y intercepts)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "you now have the center(0,0), vertices(-3/2,0) and (3/2,0) and co-vertices(0,-1/9) and (0,1/9)<BR>\n" );
document.write( "with which you can draw the graph </SPAN>\n" );
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