document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183646>Question 1183646</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the ellipse x^2/9 + y^2/4 = 1 in the first quadrant. <BR>\n" );
document.write( "Lines passing through the point (3/2, 1/4), which is inside this quarter-ellipse, <BR>\n" );
document.write( "are free to pivot around it inside this region up to the y- and x-intercepts (0,2) and (3,0), respectively. <BR>\n" );
document.write( "What is the maximum or minimum area of the region that can be enclosed by the ellipse x^2/9 + y^2/4 = 1, <BR>\n" );
document.write( "any of the pivoting lines around the point (3/2, 1/4), and the x or y axis?\r<BR>\n" );
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document.write( "Thank you in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814099 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814099\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The desired area in each case illustrated below is the area of the quarter ellipse minus the area of the shaded triangle.  So, the larger the triangle, the  smaller the desired area, and the minimum triangle gives the maximum desired area and vice versa.  The area of the quarter ellipse without any subtractions is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \int_0^3\,\frac{\sqrt{36\,-\,4x^2}}{3}\,dx\">\r<BR>\n" );
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document.write( "You can use a simple trig substitution to solve this integral.  Hint: Take out the constant term and then let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 3\sin(u)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large dx\ =\ 3\cos(u)du\">\r<BR>\n" );
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document.write( "Then subtract the triangle areas illustrated:\r<BR>\n" );
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document.write( "																<BR>\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
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