document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184206>Question 1184206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the locus of point P if P be midpoint of chord joining he vertex of the parabola <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5E2+=+8x ALIGN=MIDDLE  ALT=\"+y%5E2+=+8x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to another point on it? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814742 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814742\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let (x', y') be the midpoint of the chord joining (0,0) to (x, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%282x%29 ALIGN=MIDDLE  ALT=\"2sqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) (or (x, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2sqrt%282x%29 ALIGN=MIDDLE  ALT=\"-2sqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)), which is a point on the parabola <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5E2+=+8x ALIGN=MIDDLE  ALT=\"+y%5E2+=+8x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "===> (x',y') = (x/2, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282x%29 ALIGN=MIDDLE  ALT=\"sqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "===> y' = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%2A%28x%2F2%29%29+=+2sqrt%28x%2F2%29 ALIGN=MIDDLE  ALT=\"sqrt%284%2A%28x%2F2%29%29+=+2sqrt%28x%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2√x'\r<BR>\n" );
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document.write( "===> (y')^2 = 4x'.\r<BR>\n" );
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document.write( "Therefore, the locus of the point P is the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+=+4x ALIGN=MIDDLE  ALT=\"y%5E2+=+4x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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