document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190883>Question 1190883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of the ELLIPSE that satisfies the given conditions \r<BR>\n" );
document.write( "\n" );
document.write( "d. Vertices (-5,0) and (5,0) length of latus rectum 8/5\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849182 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849182\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to find the equation of the ellipse:\r<BR>\n" );
document.write( "\n" );
document.write( "**1. Center and Orientation:**\r<BR>\n" );
document.write( "\n" );
document.write( "The vertices are at (-5,0) and (5,0).  This tells us:\r<BR>\n" );
document.write( "\n" );
document.write( "* The center of the ellipse is at the origin (0,0).<BR>\n" );
document.write( "* The major axis is horizontal (along the x-axis).\r<BR>\n" );
document.write( "\n" );
document.write( "**2. Value of 'a':**\r<BR>\n" );
document.write( "\n" );
document.write( "The distance from the center to a vertex is 'a'.  Since the vertices are at (-5,0) and (5,0), we have a = 5.\r<BR>\n" );
document.write( "\n" );
document.write( "**3. Latus Rectum:**\r<BR>\n" );
document.write( "\n" );
document.write( "The length of the latus rectum is given as 8/5. The formula for the latus rectum is (2b²)/a.\r<BR>\n" );
document.write( "\n" );
document.write( "**4. Solve for 'b²':**\r<BR>\n" );
document.write( "\n" );
document.write( "We can use the latus rectum length and the value of 'a' to solve for b²:\r<BR>\n" );
document.write( "\n" );
document.write( "8/5 = (2b²) / 5<BR>\n" );
document.write( "8 = 2b²<BR>\n" );
document.write( "b² = 4\r<BR>\n" );
document.write( "\n" );
document.write( "**5. Equation of the Ellipse:**\r<BR>\n" );
document.write( "\n" );
document.write( "Since the major axis is horizontal, the standard form of the equation is:\r<BR>\n" );
document.write( "\n" );
document.write( "(x²/a²) + (y²/b²) = 1\r<BR>\n" );
document.write( "\n" );
document.write( "Substitute the values of a² and b²:\r<BR>\n" );
document.write( "\n" );
document.write( "(x²/5²) + (y²/4) = 1<BR>\n" );
document.write( "(x²/25) + (y²/4) = 1\r<BR>\n" );
document.write( "\n" );
document.write( "Therefore, the equation of the ellipse is (x²/25) + (y²/4) = 1.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );