document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=861160>Question 861160</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the center (h,v) of the ellipse. show work <BR>\n" );
document.write( "Center:(-3,0)<BR>\n" );
document.write( "vertex1:(-3,5)<BR>\n" );
document.write( "vertex2:(-3,-5)<BR>\n" );
document.write( "focus1:(-3,4)<BR>\n" );
document.write( "focus2:(-3,-4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #518938 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=518938\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I see the answer to the question: Center:(-3,0) .<BR>\n" );
document.write( "I also see information that would allow to find the center, and the equation of the ellipse.<BR>\n" );
document.write( "I think someone typed the wrong question, and what should have been asked is \"write the equation for the ellipse\".<BR>\n" );
document.write( " <BR>\n" );
document.write( "Form the coordinates of the vertices, you can find the coordinates (h,v) of the center.<BR>\n" );
document.write( "The center is midway between the vertices, so averaging the coordinates of the vertices, you find the coordinates of the center:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=%28-3%2B%28-3%29%29%2F2=%28-6%29%2F2=-3 ALIGN=MIDDLE  ALT=\"h=%28-3%2B%28-3%29%29%2F2=%28-6%29%2F2=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (averaging the x-coordinates of the vertices),<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=%285%2B%28-5%29%29%2F2=0%2F2=0 ALIGN=MIDDLE  ALT=\"v=%285%2B%28-5%29%29%2F2=0%2F2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (averaging the y-coordinates of the vertices).<BR>\n" );
document.write( " <BR>\n" );
document.write( "Form the coordinates of the foci, you can find the coordinates (h,v) of the center (also by averaging, the same way as done for the vertices).<BR>\n" );
document.write( " <BR>\n" );
document.write( "You need all (or most) of that information to figure out the equation for the ellipse.<BR>\n" );
document.write( "Your ellipse has the center, vertices, and foci on the vertical line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-10%2C10%2C-10%2C10%2C%0D%0Ared%28arc%280%2C0%2C8%2C16%2C0%2C360%29%29%2C%0D%0Ablue%28circle%280%2C0%2C0.2%29%29%2Clocate%280.1%2C3.7%2Cblue%28c%29%29%2C%0D%0Ablue%28circle%280%2C8%2C0.2%29%29%2Cblue%28circle%280%2C-8%2C0.2%29%29%2C%0D%0Ablue%28circle%280%2C6.93%2C0.2%29%29%2Cblue%28circle%280%2C-6.93%2C0.2%29%29%2C%0D%0Ablue%28circle%284%2C0%2C0.2%29%29%2Cblue%28circle%28-4%2C0%2C0.2%29%29%2C%0D%0Ablue%28triangle%280%2C0%2C0%2C-6.93%2C4%2C0%29%29%2Cblue%28triangle%280%2C6.93%2C0%2C0%2C4%2C0%29%29%2C%0D%0Ablue%28rectangle%280%2C0%2C0.5%2C0.5%29%29%2Clocate%282.1%2C0.9%2Cblue%28b%29%29%2C%0D%0Ablue%28arrow%28-9.8%2C8%2C-0.2%2C8%29%29%2Clocate%28-9.8%2C8.9%2Cblue%28vertex%29%29%2C%0D%0Agreen%28arrow%28-6.5%2C8%2C-6.5%2C0%29%29%2Cgreen%28arrow%28-6.5%2C0%2C-6.5%2C8%29%29%2C%0D%0Agreen%28arrow%28-0.2%2C-8%2C-12%2C-8%29%29%2Clocate%28-6.6%2C4.5%2Ca%29%2Clocate%28-6.6%2C-3.5%2Ca%29%2C%0D%0Agreen%28arrow%28-6.5%2C-8%2C-6.5%2C0%29%29%2Cgreen%28arrow%28-6.5%2C0%2C-6.5%2C-8%29%29%2C%0D%0Alocate%282.1%2C4.3%2Cblue%28a%29%29%2Clocate%280.1%2C-2.5%2Cblue%28c%29%29%2C%0D%0Ablue%28arrow%286%2C6.93%2C0.2%2C6.93%29%29%2Clocate%286.1%2C7.4%2Cblue%28focus%29%29%2C%0D%0Alocate%28-3.5%2C2%2Cblue%28center%29%29%2Cblue%28arc%28-3%2C0.5%2C1%2C1%2C90%2C270%29%29%2C%0D%0Ablue%28arrow%28-3%2C0%2C-0.25%2C0%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The distance from the center to each vertex is usually called the \"semi-major axis\".<BR>\n" );
document.write( "It is represented by the letter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and in this case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5 ALIGN=MIDDLE  ALT=\"a=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The distance from the center to each focus is usually called the \"focal distance\", and is represented by the letter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "In this case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=4 ALIGN=MIDDLE  ALT=\"c=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "There is another important quantity, often called the \"semi-minor axis\", represented by the letter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The quantities <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > are related by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=b%5E2%2Bc%5E2 ALIGN=MIDDLE  ALT=\"a%5E2=b%5E2%2Bc%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this case, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5 ALIGN=MIDDLE  ALT=\"a=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=4 ALIGN=MIDDLE  ALT=\"c=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2=b%5E2%2B4%5E2 ALIGN=MIDDLE  ALT=\"5%5E2=b%5E2%2B4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=b%5E2%2B16 ALIGN=MIDDLE  ALT=\"25=b%5E2%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25-16=b%5E2 ALIGN=MIDDLE  ALT=\"25-16=b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=9 ALIGN=MIDDLE  ALT=\"b%5E2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When you know the coordinates of the center, (h,v),<BR>\n" );
document.write( "know that the major axis is vertical<BR>\n" );
document.write( "(center, vertices, and foci have the same x-coordinate),<BR>\n" );
document.write( "and know <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2 ALIGN=MIDDLE  ALT=\"b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "you can write the equation of the ellipse as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fb%5E2%2B%28y-v%29%5E2%2Fa%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fb%5E2%2B%28y-v%29%5E2%2Fa%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this case,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2%2F9%2B%28y-0%29%5E2%2F5%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2%2F9%2B%28y-0%29%5E2%2F5%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x-3%29%5E2%2F9%2By%5E2%2F25=1%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x-3%29%5E2%2F9%2By%5E2%2F25=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );