document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=901412>Question 901412</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation:<BR>\n" );
document.write( " find an equation of the set of points such that each point satisfies the given conditions.\r<BR>\n" );
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document.write( "-its distance from (0,-2) is 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #546732 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=546732\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28350%2C250%2C-0.1%2C0.6%2C-0.3%2C0.2%2Cgrid%280%29%2C%0D%0Acircle%280%2C-0.2%2C0.005%29%2Clocate%28-0.07%2C-0.21%2CC%280%2C-2%29%29%2C%0D%0Acircle%280.4%2C0.1%2C0.005%29%2Clocate%280.35%2C0.14%2CP%28x%2Cy%29%29%2C%0D%0Acircle%280.4%2C-0.2%2C0.005%29%2Clocate%280.4%2C-0.205%2CQ%28-2%2Cy%29%29%2C%0D%0Atriangle%280%2C-0.2%2C0.4%2C-0.2%2C0.4%2C0.1%29%2Clocate%280.2%2C-0.05%2C5%29%2C%0D%0Arectangle%280.4%2C-0.2%2C0.375%2C-0.175%29%2C%0D%0Alocate%280.15%2C-0.2%2C%28x-0%29%29%2Clocate%280.4%2C-0.05%2C%28y-%28-2%29%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A point P(x,y) on an x-y plane at a distance of 5 units from (0,-2) will comply with<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x-0%29%5E2%2B%28y-%28-2%29%29%5E2%29=5 ALIGN=MIDDLE  ALT=\"sqrt%28%28x-0%29%5E2%2B%28y-%28-2%29%29%5E2%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-0%29%5E2%2B%28y-%28-2%29%29%5E2=5%5E2 ALIGN=MIDDLE  ALT=\"%28x-0%29%5E2%2B%28y-%28-2%29%29%5E2=5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Maybe you are familiar with the formula on the left, which your teacher may have called \"the distance formula\".<BR>\n" );
document.write( "Or maybe you realize that you can get the equation on the right by applying the Pythagorean theorem to right triangle CPQ above. (That is the basis of \"the distance formula\", anyway).<BR>\n" );
document.write( "From the formulas above, you easily derive<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5E2%2B%28y%2B2%29%5E2=25%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5E2%2B%28y%2B2%29%5E2=25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the equation for the set of points at a distance of 5 units from C(0,-2), which is the circle of radius 5, centered at C(0,-2).<BR>\n" );
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document.write( "MORE:<BR>\n" );
document.write( "The equation above is the answer I like best, but it is not the only equation you can write. There are, of course, an infinite number of equivalent equations,  most of them ridiculously and unnecessarily complicated.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28y%2B2%29%5E2=25 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28y%2B2%29%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2B4y%2B4=25 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2B4y%2B4=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5E2%2By%5E2%2B4y-21=0%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5E2%2By%5E2%2B4y-21=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives you another reasonable option.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28y%2B2%29%5E2=25 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28y%2B2%29%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5E2%2F25%2B%28y%2B2%29%5E2%2F25=1%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5E2%2F25%2B%28y%2B2%29%5E2%2F25=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives you another reasonable option.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2B4y-21=0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2B4y-21=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%28x%5E2%2By%5E2%2B4y-21%29=100%2A0 ALIGN=MIDDLE  ALT=\"100%28x%5E2%2By%5E2%2B4y-21%29=100%2A0\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100x%5E2%2B100y%5E2%2B400y-2100=0 ALIGN=MIDDLE  ALT=\"100x%5E2%2B100y%5E2%2B400y-2100=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ia an equivalent equation, made unnecessarily complicated by multiplying times 100.<BR>\n" );
document.write( "We can multiply any equation times a non-zero number and get an equivalent equation. </SPAN>\n" );
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