document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=854642>Question 854642</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the ellipse described. Focus at (0, -3) and (0, 3) vertices at (0, 7) and (0, -7) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #514835 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=514835\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> With vertices at (0, 7) and (0, -7),<BR>\n" );
document.write( "we know that the major axis is the vertical segment connecting  (0, 7) and (0, -7),<BR>\n" );
document.write( "and that the center of the ellipse is located at (0,0),<BR>\n" );
document.write( "the midpoint of the major axis.<BR>\n" );
document.write( "We also know that the semi-major axis will be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=7 ALIGN=MIDDLE  ALT=\"a=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the distance from the center to either one of the vertices.<BR>\n" );
document.write( "We know that the focal distance is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=3 ALIGN=MIDDLE  ALT=\"c=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the distance from the center to the known focus.<BR>\n" );
document.write( "We can find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the semi-minor axis by using the known relation<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( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5E2=b%5E2%2B3%5E2 ALIGN=MIDDLE  ALT=\"7%5E2=b%5E2%2B3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49=b%5E2%2B9 ALIGN=MIDDLE  ALT=\"49=b%5E2%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49-9=b%5E2 ALIGN=MIDDLE  ALT=\"49-9=b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=40 ALIGN=MIDDLE  ALT=\"b%5E2=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the equation of an ellipse centered at the origin, with a vertical major axis is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Fb%5E2%2By%5E2%2Fa%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2Fb%5E2%2By%5E2%2Fa%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=40 ALIGN=MIDDLE  ALT=\"b%5E2=40\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=7%5E2=49 ALIGN=MIDDLE  ALT=\"a%5E2=7%5E2=49\"   DISABLED_style= \"max-width:90%; height:auto;\" > our equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5E2%2F40%2By%5E2%2F49=1%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5E2%2F40%2By%5E2%2F49=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-8%2C8%2C-8%2C8%2C%0D%0Arectangle%280%2C0%2C0.4%2C0.4%29%2Cgrid%280%29%2C%0D%0Aarc%280%2C0%2C12.64%2C14%2C0%2C360%29%2C%0D%0Aline%286.32%2C0%2C0%2C3%29%2C%0D%0Agreen%28line%28-4%2C7%2C0%2C7%29%29%2Clocate%28-3.15%2C3.8%2Ca%29%2C%0D%0Aarrow%28-3%2C4%2C-3%2C7%29%2Carrow%28-3%2C3%2C-3%2C0%29%2C%0D%0Alocate%280.1%2C2%2Cc%29%2Clocate%282.5%2C0.6%2Cb%29%2C%0D%0Alocate%282%2C2%2Ca%29%2Clocate%286.35%2C0%2Cred%28B%29%29%2C%0D%0Alocate%280.1%2C0%2Cred%28O%29%29%2Clocate%280.1%2C3.6%2Cred%28C%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <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;\" > is Pythagoras applied to triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28OBC%29 ALIGN=MIDDLE  ALT=\"red%28OBC%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );