document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208732>Question 1208732</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the ellipse with vertex at (0, 0), vertices at (3, 0) and (-3, 0), and eccentricity of 1/3. Identify the parts of the ellipse and sketch the graph. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847147 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=847147\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Find the equation of the ellipse with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28vertex%29 ALIGN=MIDDLE  ALT=\"cross%28vertex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > center at (0, 0), vertices at (3, 0) and (-3, 0), and eccentricity of 1/3. Identify the parts of the ellipse and sketch the graph.<br><BR>\n" );
document.write( "The center is at (0,0) and the vertices are at (-3,0) and (3,0), so a, the semi-major axis, is 3.<br><BR>\n" );
document.write( "The eccentricity, e = c/a, is 1/3; with a = 3, c = 1.<br><BR>\n" );
document.write( "For an ellipse, a, b, and c are related by <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;\" >.  With a=3 and c=1, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=sqrt%288%29=2sqrt%282%29 ALIGN=MIDDLE  ALT=\"b=sqrt%288%29=2sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "b is the semi-minor axis, so the covertices are (0,2sqrt(2)) and (0,-2sqrt(2))<br><BR>\n" );
document.write( "The equation of the ellipse with center (0,0), is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "center (0,0)<BR>\n" );
document.write( "vertices (-3,0) and (3,0)<BR>\n" );
document.write( "covertices (0,2sqrt(2)) and (0,-2sqrt(2))<BR>\n" );
document.write( "equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F9%2By%5E2%2F8=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F9%2By%5E2%2F8=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );