document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1086398>Question 1086398</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the area bounded by the curve x^2=8y and its latus rectum </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #700608 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=700608\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation of the parabola can be written  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%281%2F8%29x%5E2+ ALIGN=MIDDLE  ALT=\"+y+=+%281%2F8%29x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Graphed below (green line is latus rectum):<BR>\n" );
document.write( "—\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-4%2C+4%2C+-5%2C+5%2C+%281%2F8%29%2Ax%5E2%2C+y=2%29%0D%0A+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-4%2C+4%2C+-5%2C+5%2C+%281%2F8%29%2Ax%5E2%2C+y=2%29%0D%0A+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "—\r<BR>\n" );
document.write( "\n" );
document.write( "For a (vertical) parabola with vertex @(h,k):   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4p%28y-k%29+=+%28x-h%29%5E2+ ALIGN=MIDDLE  ALT=\"+4p%28y-k%29+=+%28x-h%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Vertex is at (0,0) so h=k=0:   so this parabola has equation  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%281%2F8%29x%5E2+ ALIGN=MIDDLE  ALT=\"+y+=+%281%2F8%29x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Solve for p (the distance from vertex to focus) by comparison:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+x%5E2%2F%284p%29+ ALIGN=MIDDLE  ALT=\"+y+=+x%5E2%2F%284p%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4p+=+8+ ALIGN=MIDDLE  ALT=\"+4p+=+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> p=2<BR>\n" );
document.write( "So focus is at (0,2).   Latus rectum passed through (0,2) and intersects parabola where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2+=+%281%2F8%29x%5E2+ ALIGN=MIDDLE  ALT=\"y+=+2+=+%281%2F8%29x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  (-4,2) and (4,2)\r<BR>\n" );
document.write( "\n" );
document.write( "Using just the first quadrant & symmetry with 2nd quadrant:<BR>\n" );
document.write( "Area = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A+int%28%28+2+-+%281%2F8%29x%5E2%29%2C+dx%2C+0%2C+4%29+ ALIGN=MIDDLE  ALT=\"+2%2A+int%28%28+2+-+%281%2F8%29x%5E2%29%2C+dx%2C+0%2C+4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "         = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A+%282x+-+%281%2F24%29x%5E3%29+ ALIGN=MIDDLE  ALT=\"+2%2A+%282x+-+%281%2F24%29x%5E3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  evaluated at 4 and 0<BR>\n" );
document.write( "          = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A%28%288-%281%2F24%29%2864%29%29+-+%280-0%29%29+ ALIGN=MIDDLE  ALT=\"+2%2A%28%288-%281%2F24%29%2864%29%29+-+%280-0%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=+highlight%2832%2F3%29+ ALIGN=MIDDLE  ALT=\"+highlight%2832%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );