document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=768411>Question 768411</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Idenitfy the equation AND the graph of the ellipse with foci at (0, +- 6) and vertices at (0, +- 8) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #468279 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=468279\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Identify the equation AND the graph of the ellipse with foci at (0, +- 6) and vertices at (0, +- 8)<BR>\n" );
document.write( "***<BR>\n" );
document.write( "This is an ellipse with vertical major axis. (y-coordinates of foci and vertices change but x-coordinates do not.<BR>\n" );
document.write( "Its standard form of equation: <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( "For given ellipse:<BR>\n" );
document.write( "y-coordinate of center=0 (midpoint of foci or vertices)<BR>\n" );
document.write( "x-coordinate=0<BR>\n" );
document.write( "center: (0,0)<BR>\n" );
document.write( "a=8 (distance from center to vertices)<BR>\n" );
document.write( "a^2=64<BR>\n" );
document.write( "c=6 (distance from center to foci)<BR>\n" );
document.write( "c^2=36<BR>\n" );
document.write( "c^2=a^2-b^2<BR>\n" );
document.write( "b^2=a^2-c^2=64-36=28<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F28%2By%5E2%2F64=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F28%2By%5E2%2F64=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "see graph below:<BR>\n" );
document.write( "y=±(64-16x^2/7)^.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+%2864-16x%5E2%2F7%29%5E.5%2C-%2864-16x%5E2%2F7%29%5E.5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );