document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=848401>Question 848401</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the equation of the ellipse having the following properties :<BR>\n" );
document.write( "1. center at (3,5), vertex at (-2,5) focus at (6,5).<BR>\n" );
document.write( "2.Center at (2,3) vertex at (2,-1) and LR=9/2<BR>\n" );
document.write( "3. center at origin, focus at (squareroot of 3,0) passing through (1, squareroot of 3/2)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #511277 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=511277\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find the equation of the ellipse having the following properties :<BR>\n" );
document.write( "1. center at (3,5), vertex at (-2,5) focus at (6,5).<BR>\n" );
document.write( "2.Center at (2,3) vertex at (2,-1) and LR=9/2<BR>\n" );
document.write( "3. center at origin, focus at (squareroot of 3,0) passing through (1, squareroot of 3/2)<BR>\n" );
document.write( "***<BR>\n" );
document.write( "Standard form of equation for an ellipse with horizontal major axis:<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( "Standard form of equation for an ellipse with vertical major axis: <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( "1. center at (3,5), vertex at (-2,5) focus at (6,5).<BR>\n" );
document.write( "Ellipse has a horizontal major axis.<BR>\n" );
document.write( "center: (3,5)<BR>\n" );
document.write( "a=5 (distance from center to vertices)<BR>\n" );
document.write( "a^2=25<BR>\n" );
document.write( "c=3<BR>\n" );
document.write( "c^2=9<BR>\n" );
document.write( "c^2=a^2-b^2<BR>\n" );
document.write( "b^2=a^2-c^2=25-9=16<BR>\n" );
document.write( "Equation of given ellipse:<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2%2F25%2B%28y-5%29%5E2%2F16=1 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2%2F25%2B%28y-5%29%5E2%2F16=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "2.Center at (2,3) vertex at (2,-1) and LR=9/2<BR>\n" );
document.write( "Ellipse has a vertical major axis.<BR>\n" );
document.write( "center:(2,3)<BR>\n" );
document.write( "a=4 (3 to -1) and (3 to 7)(center to vertices)<BR>\n" );
document.write( "a^2=16<BR>\n" );
document.write( "latus rectum=2b^2/a=2b^2/4=b^2/2<BR>\n" );
document.write( "b^2/2=9/2<BR>\n" );
document.write( "b^2=9<BR>\n" );
document.write( "Equation of given ellipse:<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2F9%2B%28y-3%29%5E2%2F16=1 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2F9%2B%28y-3%29%5E2%2F16=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "3. center at origin, focus at (squareroot of 3,0) passing through (1, squareroot of 3/2)<BR>\n" );
document.write( "Repost for another smarter tutor to solve.\r<BR>\n" );
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