document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=989017>Question 989017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this!. A circle passes through the points (-3,1) and (-1,5). Its centre lies on the x-axis. Find (a) the coordinates of the centre, (b) the equation of the circle and (c) if the point (1,p) also lies on this circle, find the possible values of p (leaving your answers in surd form if necessary). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #609460 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=609460\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "(a)<BR>\n" );
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document.write( "Standard form for circle:<BR>\n" );
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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" );
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document.write( "We know k=0, since center is on x axis. Using point (-3,1):<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3-h%29%5E2%2B%281-0%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28-3-h%29%5E2%2B%281-0%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=9%2B6h%2Bh%5E2%2B1=r%5E2 ALIGN=MIDDLE  ALT=\"9%2B6h%2Bh%5E2%2B1=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=h%5E2%2B6h%2B10=r%5E2 ALIGN=MIDDLE  ALT=\"h%5E2%2B6h%2B10=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Using point (-1,5)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1-h%29%5E2%2B%285-0%29%5E2=r%5E2%0D%0A%7B%7B%7B1%2B2h%2Bh%5E2%2B25=r%5E2 ALIGN=MIDDLE  ALT=\"%28-1-h%29%5E2%2B%285-0%29%5E2=r%5E2%0D%0A%7B%7B%7B1%2B2h%2Bh%5E2%2B25=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=h%5E2%2B2h%2B26=r%5E2 ALIGN=MIDDLE  ALT=\"h%5E2%2B2h%2B26=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since both =r^2:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2%2B6h%2B10=h%5E2%2B2h%2B26 ALIGN=MIDDLE  ALT=\"h%5E2%2B6h%2B10=h%5E2%2B2h%2B26\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4h-16=0 ALIGN=MIDDLE  ALT=\"4h-16=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4h=16 ALIGN=MIDDLE  ALT=\"4h=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=4 ALIGN=MIDDLE  ALT=\"h=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "ANSWER (a): Co-ordinates of the center: (h,k)=(4,0)<BR>\n" );
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document.write( "(b) Find the equation:<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;\" > (h,k)=(4,0)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2%2B%28y-0%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2%2B%28y-0%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use point (-3,1) to find r^2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3-4%29%5E2%2B%281-0%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28-3-4%29%5E2%2B%281-0%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=%28-7%29%5E2%2B%281%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28-7%29%5E2%2B%281%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=49%2B1=r%5E2 ALIGN=MIDDLE  ALT=\"49%2B1=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=50=r%5E2 ALIGN=MIDDLE  ALT=\"50=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "ANSWER:(b): Equation of circle: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2%2By%5E2=50 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2%2By%5E2=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "(c) Point (1,p)<BR>\n" );
document.write( "Using value (1)for x (p=y):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-4%29%5E2%2By%5E2=50 ALIGN=MIDDLE  ALT=\"%281-4%29%5E2%2By%5E2=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%5E2%2By%5E2=50 ALIGN=MIDDLE  ALT=\"%28-3%29%5E2%2By%5E2=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2By%5E2=50 ALIGN=MIDDLE  ALT=\"9%2By%5E2=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=41 ALIGN=MIDDLE  ALT=\"y%5E2=41\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >=(+ or -)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2841%29 ALIGN=MIDDLE  ALT=\"sqrt%2841%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "ANSWER: Possible values of p are (+ or -)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2841%29 ALIGN=MIDDLE  ALT=\"sqrt%2841%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );