document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=934410>Question 934410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The point P moves along an arc of a circle with centre E(2, 3). the arc of the circle passes through A(-2, 0) and B(5, k). <BR>\n" );
document.write( "(a) Find<BR>\n" );
document.write( "(i) the equation of the locus of the point P,<BR>\n" );
document.write( "(ii) the values of k. <BR>\n" );
document.write( "(b) The tangent of the circle at the point A intersects the y-axis at the point Q. Find the area of the triangle OAQ where Of is the origin. <BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #568915 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=568915\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The general equation of a circle is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2B%28y-k%29%5E2=R%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2B%28y-k%29%5E2=R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2B%28y-3%29%5E2=R%5E2 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2B%28y-3%29%5E2=R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use A to get R.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2-2%29%5E2%2B%280-3%29%5E2=R%5E2 ALIGN=MIDDLE  ALT=\"%28-2-2%29%5E2%2B%280-3%29%5E2=R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2B9=R%5E2 ALIGN=MIDDLE  ALT=\"16%2B9=R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2=25 ALIGN=MIDDLE  ALT=\"R%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=5 ALIGN=MIDDLE  ALT=\"R=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2B%28y-3%29%5E2=25 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2B%28y-3%29%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285-2%29%5E2%2B%28k-3%29%5E2=25 ALIGN=MIDDLE  ALT=\"%285-2%29%5E2%2B%28k-3%29%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2B%28k-3%29%5E2=25 ALIGN=MIDDLE  ALT=\"9%2B%28k-3%29%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k-3%29%5E2=16 ALIGN=MIDDLE  ALT=\"%28k-3%29%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k-3=+0+%2B-+4 ALIGN=MIDDLE  ALT=\"k-3=+0+%2B-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=3+%2B-+4 ALIGN=MIDDLE  ALT=\"k=3+%2B-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-1 ALIGN=MIDDLE  ALT=\"k=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=7 ALIGN=MIDDLE  ALT=\"k=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-2%29dx%2B2%28y-3%29dy=0 ALIGN=MIDDLE  ALT=\"2%28x-2%29dx%2B2%28y-3%29dy=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-3%29dy=-%28x-2%29dx ALIGN=MIDDLE  ALT=\"%28y-3%29dy=-%28x-2%29dx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=-%28x-2%29%2F%28y-3%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=-%28x-2%29%2F%28y-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At A,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=-%28-2-2%29%2F%280-3%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=-%28-2-2%29%2F%280-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=-%284%2F3%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=-%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-5%2C5%2Cgrid%281%29%2Cblue%28line%28-2%2C0%2C2%2C-5%29%29%2Ccircle%282%2C3%2C5%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The value of the derivative is equal to the slope of the tangent line.<BR>\n" );
document.write( "Using the point-slope form of a line,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-0=-%284%2F3%29%28x-%28-2%29%29 ALIGN=MIDDLE  ALT=\"y-0=-%284%2F3%29%28x-%28-2%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=y=-%284%2F3%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"y=-%284%2F3%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%284%2F3%29%282%29 ALIGN=MIDDLE  ALT=\"y=-%284%2F3%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=y=-8%2F3 ALIGN=MIDDLE  ALT=\"y=-8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So know you know the base and height of the triangle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%281%2F2%29%282%29%288%2F3%29 ALIGN=MIDDLE  ALT=\"A=%281%2F2%29%282%29%288%2F3%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=8%2F3 ALIGN=MIDDLE  ALT=\"A=8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );