document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136776>Question 1136776</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello! If someone could please help me solve this equation, I would be very grateful.\r<BR>\n" );
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document.write( "Find an equation for the ellipse with vertices at (-3, 4) and (15, 4); focus at (13, 4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754596 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=754596\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Since you asked for help, that's exactly what I will do -- show you what you need to do to find the equation.  Then, doing the work yourself, you will learn something from it.<br><BR>\n" );
document.write( "The standard form of the equation of an ellipse with horizontal major axis centered at (h,k) is<br><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;\" ><br><BR>\n" );
document.write( "In that formula, a is the semi-major axis (from the center of the ellipse to each end of the major axis) and b is the semi-minor axis (from the center to each end of the minor axis).<br><BR>\n" );
document.write( "The two given vertices are the ends of the major axis; from that information you can determine the center of the ellipse (halfway between the two vertices) and the value of a (distance from the center to each vertex).<br><BR>\n" );
document.write( "The only thing left you need to write the equation is the value of b.<br><BR>\n" );
document.write( "The distance from the center of the ellipse to each focus is c, where a, b, and c are related by<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+a%5E2-b%5E2 ALIGN=MIDDLE  ALT=\"c%5E2+=+a%5E2-b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Since you now know the center of the ellipse, the given coordinates of a focus allow you to determine the value of c; and from that you can determine the value of b.<br><BR>\n" );
document.write( "Then you will have all you need to write the equation.<br><BR>\n" );
document.write( "Good luck finishing.<br><BR>\n" );
document.write( "If you need help finishing, post a \"thank you\" message indicating what progress you have made and where you need help. </SPAN>\n" );
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