document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=835350>Question 835350</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hey. My name is Anne. Nice to meet your lovely self. ^_^<BR>\n" );
document.write( "Conics confuse me completely. Right now my class is on ellipses. So my question is how do I find an equation of an ellipse? It gave me a graph, and a couple points. The major axis is vertical, and the vertex is (0,10) and (0,-10). The focus is at (0,8) and (0,-8).<BR>\n" );
document.write( "I know there's some kind of equation to put these numbers in, but somehow that did not end up in my notes! :(<BR>\n" );
document.write( "While I'm asking, how would I do this when the major axis is horizontal? (I know that's asking 2 questions. I understand if you can't, or won't answer that one. I just need the equation.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #503463 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=503463\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How do I find an equation of an ellipse? It gave me a graph, and a couple points. The major axis is vertical, and the vertex is (0,10) and (0,-10). The focus is at (0,8) and (0,-8).<BR>\n" );
document.write( "***<BR>\n" );
document.write( "When trying to find the equation for a given ellipse, you must first determine whether it has a vertical or horizontal major axis.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "If major axis is vertical,<BR>\n" );
document.write( "Standard form of equation for the ellipse: <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( "..<BR>\n" );
document.write( "If major axis is horizontal,<BR>\n" );
document.write( "Standard form of equation for the ellipse: <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( "(notice the only change is a^2 and b^2 swapping places)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Now, for your given ellipse problem:<BR>\n" );
document.write( "Gleaned from the 2 given points of the vertex,<BR>\n" );
document.write( "x-coordinate of center=0<BR>\n" );
document.write( "y-coordinate of center=0<BR>\n" );
document.write( "so,center(0,0)<BR>\n" );
document.write( "a=10(given distance from center to vertices on the vertical major axis)<BR>\n" );
document.write( "a^2=100<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c=8(given distance from center to foci on the vertical major axis)<BR>\n" );
document.write( "c^2=64<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c^2=a^2-b^2<BR>\n" );
document.write( "b^2=a^2-c^2=100-64=36<BR>\n" );
document.write( "b=&#8730;36=6<BR>\n" );
document.write( "..<BR>\n" );
document.write( "equation: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-0%29%5E2%2Fb%5E2%2B%28y-0%29%5E2%2Fa%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-0%29%5E2%2Fb%5E2%2B%28y-0%29%5E2%2Fa%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F36%2By%5E2%2F100=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F36%2By%5E2%2F100=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );