document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205643>Question 1205643</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all points satisfying x+y=0 that are 8 units from (-2,3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842577 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=842577\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Points that are 8 units from (-2,3) are on the circle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2%2B%28y-3%29%5E2+=+64 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2%2B%28y-3%29%5E2+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve x+y = 0 for y to get y = -x\r<BR>\n" );
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document.write( "Plug y = -x into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2%2B%28y-3%29%5E2+=+64 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2%2B%28y-3%29%5E2+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2%2B%28-x-3%29%5E2+=+64 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2%2B%28-x-3%29%5E2+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Do a bit of algebra to get the following<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2%2B%28-x-3%29%5E2+=+64 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2%2B%28-x-3%29%5E2+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x%2B4%2Bx%5E2%2B6x%2B9+=+64 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x%2B4%2Bx%5E2%2B6x%2B9+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x%2B4%2Bx%5E2%2B6x%2B9-64+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x%2B4%2Bx%5E2%2B6x%2B9-64+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B10x-51+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B10x-51+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now apply the quadratic formula with: a = 2, b = 10, c = -51\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10%2B-sqrt%28%2810%29%5E2-4%282%29%28-51%29%29%29%2F%282%282%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-10%2B-sqrt%28%2810%29%5E2-4%282%29%28-51%29%29%29%2F%282%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10%2B-sqrt%28100+%2B+408%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%28-10%2B-sqrt%28100+%2B+408%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10%2B-sqrt%28508%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%28-10%2B-sqrt%28508%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10%2B-++22.538855%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%28-10%2B-++22.538855%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10%2B22.538855%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%28-10%2B22.538855%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10-22.538855%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%28-10-22.538855%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812.538855%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%2812.538855%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-32.538855%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%28-32.538855%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3.134714 ALIGN=MIDDLE  ALT=\"x+=+3.134714\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-8.134714 ALIGN=MIDDLE  ALT=\"x+=+-8.134714\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Each decimal value is approximate.\r<BR>\n" );
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document.write( "Each of those x values is plugged into y = -x to find their corresponding paired y value.\r<BR>\n" );
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document.write( "The two answer points are approximately <font color=red>(3.134714, -3.134714)</font> and <font color=red>(-8.134714, 8.134714)</font> which I've marked as points A and B respectively.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28500%2C500%2C-10%2C10%2C-7%2C13%2C%0D%0Agraph%28500%2C500%2C-10%2C10%2C-7%2C13%2C-100%2C-x%29%2C%0D%0A%0D%0Acircle%28-2%2C3%2C8%29%2C%0D%0A%0D%0Acircle%283.134714%2C-3.134714%2C0.05%29%2Ccircle%283.134714%2C-3.134714%2C0.07%29%2Ccircle%283.134714%2C-3.134714%2C0.09%29%2Ccircle%283.134714%2C-3.134714%2C0.11%29%2Ccircle%283.134714%2C-3.134714%2C0.13%29%2Ccircle%283.134714%2C-3.134714%2C0.15%29%2Ccircle%28-8.134714%2C8.134714%2C0.05%29%2Ccircle%28-8.134714%2C8.134714%2C0.07%29%2Ccircle%28-8.134714%2C8.134714%2C0.09%29%2Ccircle%28-8.134714%2C8.134714%2C0.11%29%2Ccircle%28-8.134714%2C8.134714%2C0.13%29%2Ccircle%28-8.134714%2C8.134714%2C0.15%29%2C%0D%0A%0D%0Acircle%28-2%2C3%2C0.05%29%2Ccircle%28-2%2C3%2C0.07%29%2Ccircle%28-2%2C3%2C0.09%29%2Ccircle%28-2%2C3%2C0.11%29%2Ccircle%28-2%2C3%2C0.13%29%2Ccircle%28-2%2C3%2C0.15%29%2C%0D%0A%0D%0Alocate%283.134714%2C-3.134714-0.2%2C%22A%22%29%2C%0D%0Alocate%28-8.134714%2C8.134714-0.2%2C%22B%22%29%2C%0D%0Alocate%28-2%2C3-0.2%2C%22C%22%29%0D%0A%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Point A is located at roughly (3.134714, -3.134714)<BR>\n" );
document.write( "Point B is located at roughly (-8.134714, 8.134714)<BR>\n" );
document.write( "Point C is the center of the circle which is (-2,3)<BR>\n" );
document.write( "AC = 8 and BC = 8 since any point on the circle is 8 units from point C.<BR>\n" );
document.write( "Desmos and GeoGebra are two graphing tools I recommend.<BR>\n" );
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