document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1065504>Question 1065504</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An ellipse with center (4, 2) and focus (7, 2) is tangent to the y-axis.  Find the length of the minor axis. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #680743 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=680743\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The major axis,<BR>\n" );
document.write( "containing center (4,2) and focus (7,2),<BR>\n" );
document.write( "is part of line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The focal distance is the distance between center and focus,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=7-4=3 ALIGN=MIDDLE  ALT=\"c=7-4=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "There is another focus on the major axis,<BR>\n" );
document.write( "with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=4-3=1%2Cy=2%29 ALIGN=MIDDLE  ALT=\"system%28x=4-3=1%2Cy=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The ellipse looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C225%2C-1%2C9%2C-2%2C5.5%2C%0D%0Agrid%281%29%2Cred%28circle%284%2C2%2C0.1%29%29%2C%0D%0Ared%28circle%287%2C2%2C0.1%29%29%2Cred%28circle%281%2C2%2C0.1%29%29%2C%0D%0Ared%28arc%284%2C2%2C8%2C2sqrt%287%29%2C0%2C360%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > It is tangent to the y-axis<BR>\n" );
document.write( "at vertex (0,2) ,<BR>\n" );
document.write( "because an ellipse with a horizontal major axis<BR>\n" );
document.write( "can only be tangent to a vertical line at a vertex.<BR>\n" );
document.write( "So,the semi-major axis length is<BR>\n" );
document.write( "the distance from that vertex to the center,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4-0=4 ALIGN=MIDDLE  ALT=\"a=4-0=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "&#372;e know that the length of the semi-minor axis, <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( "is related to <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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2Bc%5E2=A%5E2 ALIGN=MIDDLE  ALT=\"b%5E2%2Bc%5E2=A%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=b%5E2%2B3%5E2=4%5E2 ALIGN=MIDDLE  ALT=\"b%5E2%2B3%5E2=4%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%2B9=16 ALIGN=MIDDLE  ALT=\"b%5E2%2B9=16\"   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=16-9 ALIGN=MIDDLE  ALT=\"b%5E2=16-9\"   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=7 ALIGN=MIDDLE  ALT=\"b%5E2=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=sqrt%287%29 ALIGN=MIDDLE  ALT=\"b=sqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, the length of the minor axis is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282sqrt%287%29%29 ALIGN=MIDDLE  ALT=\"highlight%282sqrt%287%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );