document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103468>Question 103468</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Thank you thank you thank you for all your assistance,,,love and light- Namaste!\r<BR>\n" );
document.write( "\n" );
document.write( "Find the eccentricity and identify the graph of the conic: r= (6)/(2+4sin theta) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75901 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=75901\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Using EXCEL, the formula, and the chart wizard, this formula yields a hyperbola. <BR>\n" );
document.write( "A conic in polar coordinates has the following form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+pe%2F%281%2B-+e+sin%28%28theta%29%29%29 ALIGN=MIDDLE  ALT=\"r+=+pe%2F%281%2B-+e+sin%28%28theta%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where p is the directix and e is the eccentricity. <BR>\n" );
document.write( "Your equation is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=+%286%29%2F%282%2B4+sin+%28theta%29%29 ALIGN=MIDDLE  ALT=\"r=+%286%29%2F%282%2B4+sin+%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=+%283%29%2F%281%2B2+sin+%28theta%29%29 ALIGN=MIDDLE  ALT=\"r=+%283%29%2F%281%2B2+sin+%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take 2 out of numerator and denominator. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e=2 ALIGN=MIDDLE  ALT=\"e=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Compare to polar conic form. <BR>\n" );
document.write( "sin(theta) in the denominator denotes a vertical transverse axis. <BR>\n" );
document.write( "e>1 denotes a hyperbola. <BR>\n" );
document.write( "The directrix lies on y=p or y=3/2. <BR>\n" );
document.write( "The conic is a hyperbola with eccentricity, e=2, and directrix of y=p.<BR>\n" );
document.write( "   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );