document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=540637>Question 540637</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rather confused about what's going on here.  My book doesn't offer an explanation on what I should do with this type of set up. \r<BR>\n" );
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document.write( "Write an equation for each ellipse.\r<BR>\n" );
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document.write( "\"foci at (-3,-3), (7,-3); the point (2,-7) on ellipse\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #353875 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=353875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write an equation for each ellipse. <BR>\n" );
document.write( "\"foci at (-3,-3), (7,-3); the point (2,-7) on ellipse<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Given data shows equation is that of an ellipse with horizontal major axis of the standard form<BR>\n" );
document.write( "(x-h)^2/a^2+(y-k)^2/b^2=1, a>b, (h,k) being the (x,y) coordinates of the center. (x-coordinates of foci changes while y-coordinates do not).<BR>\n" );
document.write( "..<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "x-coordinate of center=(7+(-3))/2=4/2=2<BR>\n" );
document.write( "y-coordinate of center=-3<BR>\n" );
document.write( "center:(2,-3)<BR>\n" );
document.write( "c=distance from center to focus on major axis=5<BR>\n" );
document.write( "c^2=25<BR>\n" );
document.write( "..<BR>\n" );
document.write( "solving for a and b in standard form of equation for ellipse:<BR>\n" );
document.write( "Sum of the distance from point (2,-7) on ellipse to each of the two focal points=2a<BR>\n" );
document.write( "Using distance formula:&#8730;[(x1-x2)^2+(y1-y^2)^2]+&#8730;[(x1-x2)^2+(y1-y^2)^2]=2a<BR>\n" );
document.write( "&#8730;[(2+3)^2+(-7+3)^2]+&#8730;[(2-7)^2+(-7+3)^2]=2a<BR>\n" );
document.write( "&#8730;[(5)^2+(-4)^2]+&#8730;[(-5)^2+(-4)^2]=2a<BR>\n" );
document.write( "&#8730;[25+16]+&#8730;[25+16]=2a<BR>\n" );
document.write( "&#8730;[41]+&#8730;[41]=2&#8730;41=2a<BR>\n" );
document.write( "a=&#8730;41<BR>\n" );
document.write( "a^2=41<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c^2=a^2-b^2<BR>\n" );
document.write( "b^2=a^2-c^2=41-25=16<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation of given ellipse:<BR>\n" );
document.write( "(x-2)^2/41+(y+3)^2/16=1 </SPAN>\n" );
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