document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1055387>Question 1055387</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The graph of |x|+|2y|=c where c>0 meets the ellipse x^2+ 4y^2 =16 in exactly 4 points. Determine the area of the convex quadrilateral with these four points as vertices. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #670658 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=670658\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Fombitz&illustration_name=lp11.JPG\">.<BR>\n" );
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document.write( ".Plotting the graph of the ellipse and the function shows that if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%3C2 ALIGN=MIDDLE  ALT=\"c%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" > the four lines lie within the ellipse and does not intersect the ellipse. If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%3E5.66 ALIGN=MIDDLE  ALT=\"c%3E5.66\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the lines also do not intersect the ellipse. For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%3Cc%3C5.66 ALIGN=MIDDLE  ALT=\"4%3Cc%3C5.66\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the lines intersect the ellipse in 8 points. The only value where there are 4 points of intersection is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=4 ALIGN=MIDDLE  ALT=\"c=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "At that point, it's the sum of 4 triangle areas with a base of 4 and height of 2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4%2A%281%2F2%29%284%29%282%29 ALIGN=MIDDLE  ALT=\"A=4%2A%281%2F2%29%284%29%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=16%29 ALIGN=MIDDLE  ALT=\"A=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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