document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140692>Question 1140692</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the eccentricity, the type of conic, and the directrix.\r<BR>\n" );
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document.write( "r = (9)/(5 +6 cos θ) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #761377 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=761377\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+9%2F%285+%2B6cos%28theta%29%29+ ALIGN=MIDDLE  ALT=\"r+=+9%2F%285+%2B6cos%28theta%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "find: <BR>\n" );
document.write( "the type of conic <BR>\n" );
document.write( "the eccentricity<BR>\n" );
document.write( " the directrix:\r<BR>\n" );
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document.write( "Standard form for conics in polar equations is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=%28ep%29%2F%281+%2B-+e%2Acos%28theta%29%29 ALIGN=MIDDLE  ALT=\"r+=%28ep%29%2F%281+%2B-+e%2Acos%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e ALIGN=MIDDLE  ALT=\"e\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the eccentricity, the directrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = ±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" > if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cosine ALIGN=MIDDLE  ALT=\"cosine\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "in your case:  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+9%2F%285+%2B6cos%28theta%29%29 ALIGN=MIDDLE  ALT=\"r+=+9%2F%285+%2B6cos%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  multiply the numerator and denominator by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5 ALIGN=MIDDLE  ALT=\"1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+9%281%2F5%29%2F%285%281%2F5%29+%2B%281%2F5%296cos%28theta%29%29 ALIGN=MIDDLE  ALT=\"r+=+9%281%2F5%29%2F%285%281%2F5%29+%2B%281%2F5%296cos%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%289%2F5%29%2F%281+%2B%286%2F5%29cos%28theta%29%29+ ALIGN=MIDDLE  ALT=\"r+=+%289%2F5%29%2F%281+%2B%286%2F5%29cos%28theta%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the eccentricity:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e=6%2F5 ALIGN=MIDDLE  ALT=\"e=6%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the directrix:\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ep=9%2F5 ALIGN=MIDDLE  ALT=\"ep=9%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=%289%2F5%29%2Fe ALIGN=MIDDLE  ALT=\"p=%289%2F5%29%2Fe\"   DISABLED_style= \"max-width:90%; height:auto;\" >...substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e ALIGN=MIDDLE  ALT=\"e\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=%289%2F5%29%2F%286%2F5%29 ALIGN=MIDDLE  ALT=\"p=%289%2F5%29%2F%286%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=%289%2F6%29 ALIGN=MIDDLE  ALT=\"p=%289%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=%283%2F2%29 ALIGN=MIDDLE  ALT=\"p=%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, the directrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+p+ ALIGN=MIDDLE  ALT=\"x+=+p+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "the type of conic:\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%3E1 ALIGN=MIDDLE  ALT=\"e%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+hyperbola ALIGN=MIDDLE  ALT=\"+hyperbola\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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