document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=692187>Question 692187</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I wonder if someone can help me on this homework problem?\r<BR>\n" );
document.write( "\n" );
document.write( "Find the vertices, foci, and eccentricity of the ellipse.  Determine lengths of major and minor axes, and sketch the graph.  \r<BR>\n" );
document.write( "\n" );
document.write( "{{xˆ2+4yˆ2=1}}\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "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 #426980 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=426980\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the vertices, foci, and eccentricity of the ellipse. Determine lengths of major and minor axes, and sketch the graph. <BR>\n" );
document.write( "{{xˆ2+4yˆ2=1}}<BR>\n" );
document.write( "**<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( "Rewrite given equation into standard form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F1%2By%5E2%2F%281%2F4%29=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F1%2By%5E2%2F%281%2F4%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "center:0,0)<BR>\n" );
document.write( "a^2=1<BR>\n" );
document.write( "a=1<BR>\n" );
document.write( "length of major axis = 2a=2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b^2=1/4<BR>\n" );
document.write( "b=1/2<BR>\n" );
document.write( "length of minor axis=2b=1<BR>\n" );
document.write( "see graph below:<BR>\n" );
document.write( "y=±(1/4-x^2/4)^.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-2%2C+2%2C+-2%2C+2%2C%281%2F4-x%5E2%2F4%29%5E.5%2C-%281%2F4-x%5E2%2F4%29%5E.5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );