document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=774946>Question 774946</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a point is at a distance 4 sqrt of 2 units from (-3/2,-5/2) and at a distance 2 sqrt of 5 units from (9/2,-5/2), find the point </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #472551 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=472551\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> [ a point is at a distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4sqrt%282%29 ALIGN=MIDDLE  ALT=\"4sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > units from (-3/2,-5/2) and at a distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > units from (9/2,-5/2), find the point ]\r<BR>\n" );
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document.write( "This point is unknown (x,y).\r<BR>\n" );
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document.write( "Look for one or two triangles with one side <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F2-%28-3%2F2%29 ALIGN=MIDDLE  ALT=\"9%2F2-%28-3%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > units long, and two other sides which are the two given lengths:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%282%29=sqrt%28%28x-%28-3%2F2%29%29%5E2%2B%28y-%28-5%2F2%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%282%29=sqrt%28%28x-%28-3%2F2%29%29%5E2%2B%28y-%28-5%2F2%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%282%29=sqrt%28%28x%2B3%2F2%29%5E2%2B%28y%2B5%2F2%29%5E2%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%282%29=sqrt%28%28x%2B3%2F2%29%5E2%2B%28y%2B5%2F2%29%5E2%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=%28x%2B3%2F2%29%5E2%2B%28y%2B5%2F2%29%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%2832=%28x%2B3%2F2%29%5E2%2B%28y%2B5%2F2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >_______We can make more use of this one.<BR>\n" );
document.write( "which is a circle\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%285%29=sqrt%28%28x-9%2F2%29%5E2%2B%28y-%28-5%2F2%29%29%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%285%29=sqrt%28%28x-9%2F2%29%5E2%2B%28y-%28-5%2F2%29%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%2820=%28x-9%2F2%29%5E2%2B%28y%2B5%2F2%29%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%2820=%28x-9%2F2%29%5E2%2B%28y%2B5%2F2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >_______ .<BR>\n" );
document.write( "also a circle\r<BR>\n" );
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document.write( "These two circles both contain the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B5%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"%28y%2B5%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which give us a way to relate them.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32-%28x%2B3%2F2%29%5E2=20-%28x-9%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"32-%28x%2B3%2F2%29%5E2=20-%28x-9%2F2%29%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-9%2F2%29%5E2-%28x%2B3%2F2%29%5E2-20+%2B32=0 ALIGN=MIDDLE  ALT=\"%28x-9%2F2%29%5E2-%28x%2B3%2F2%29%5E2-20+%2B32=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-%2818%2F2%29x%2B81%2F4-%28x%5E2%2B%286%2F2%29x%2B9%2F4%29%2B12=0 ALIGN=MIDDLE  ALT=\"x%5E2-%2818%2F2%29x%2B81%2F4-%28x%5E2%2B%286%2F2%29x%2B9%2F4%29%2B12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-9x%2B81%2F4-%28x%5E2%2B6x%2B9%2F4%29%2B12=0 ALIGN=MIDDLE  ALT=\"x%5E2-9x%2B81%2F4-%28x%5E2%2B6x%2B9%2F4%29%2B12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9x%2B81%2F4-6x-9%2F4%2B12=0 ALIGN=MIDDLE  ALT=\"-9x%2B81%2F4-6x-9%2F4%2B12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15x%2B12%2B72%2F4=0 ALIGN=MIDDLE  ALT=\"-15x%2B12%2B72%2F4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15x%2B12%2B18=0 ALIGN=MIDDLE  ALT=\"-15x%2B12%2B18=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x=30 ALIGN=MIDDLE  ALT=\"15x=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=2%29 ALIGN=MIDDLE  ALT=\"highlight%28x=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "What you now want to do, is go back to this same circle equation, solve it for y, and assign x=2 and find the value for y.  You will get two solutions for this y.  Whatever y is found to be, the two points wanted will be (2, y) and (2, -y).<BR>\n" );
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