document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=967343>Question 967343</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Eliminate the parameter in the following set of parametric equations to find a Cartesian equation of the curve.<BR>\n" );
document.write( "Graph the curve that the parametric equations represent and indicate the orientation. What type of conic section<BR>\n" );
document.write( "does the curve represent?\r<BR>\n" );
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document.write( "        x = 3 + 2 sin(t)       y = 3 cos(t)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #591291 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=591291\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sin(t) = (x-3)/2\r<BR>\n" );
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document.write( "cos(t) = y/3\r<BR>\n" );
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document.write( "sin^2(t) + cos^2(t) = 1 becomes:\r<BR>\n" );
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document.write( "((x-3)/2)^2 + (y/3)^2 = 1 which becomes:\r<BR>\n" );
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document.write( "(x-3)^2 / 2^2 + y^2 / 3^2 = 1 which becomes:\r<BR>\n" );
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document.write( "(x-3)^2 / 4 + y^2 / 9 = 1\r<BR>\n" );
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document.write( "this looks like it's the equation of an ellipse.\r<BR>\n" );
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document.write( "the graph of that equation is shown below:\r<BR>\n" );
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document.write( "in the graph, 3 (x,y) pairs were shown to be on the graph of the equation.\r<BR>\n" );
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document.write( "these points were derived from the parametric equations for x and y.\r<BR>\n" );
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document.write( "this confirmed that the graph is an accurate representation of the parametric equations.\r<BR>\n" );
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document.write( "the 3 points were based on t = 0, t = 45 degrees, t = 270 degrees.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/050101.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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