document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137032>Question 1137032</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the equation describing all points equidistant from the x-axis and the point (0,2)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754870 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=754870\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find an equation describing all points equidistant from the x-axis and the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >). \r<BR>\n" );
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document.write( "First, see if you can sketch a picture of what this curve ought to look like. <BR>\n" );
document.write( "For a point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >) that is on the curve, explain why <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28y%5E2%29=+sqrt%28x%5E2+-+%28y+-+2%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28y%5E2%29=+sqrt%28x%5E2+-+%28y+-+2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "note: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28y%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the distance from  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >) to the x-axis<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2+-+%28y+-+2%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2+-+%28y+-+2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the distance from   (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >) to the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "distances must be equal because is given:all points equidistant from the x-axis and the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Square both sides of this equation and solve for<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y ALIGN=MIDDLE  ALT=\"+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Identify the curve. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=+x%5E2+-+%28y+-+2%29%5E2 ALIGN=MIDDLE  ALT=\"y%5E2=+x%5E2+-+%28y+-+2%29%5E2\"   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=y%5E2=+x%5E2+-+%28y%5E2+-+4y%2B4%29 ALIGN=MIDDLE  ALT=\"y%5E2=+x%5E2+-+%28y%5E2+-+4y%2B4%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=y%5E2=+x%5E2+-+y%5E2+%2B4y-4 ALIGN=MIDDLE  ALT=\"y%5E2=+x%5E2+-+y%5E2+%2B4y-4\"   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=2y%5E2-4y=+x%5E2++-4 ALIGN=MIDDLE  ALT=\"2y%5E2-4y=+x%5E2++-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >......complete square for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   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=2%28y%5E2-2y%2Bb%5E2%29-2b%5E2=+x%5E2++-4 ALIGN=MIDDLE  ALT=\"2%28y%5E2-2y%2Bb%5E2%29-2b%5E2=+x%5E2++-4\"   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=2%28y%5E2-2y%2B1%5E2%29-2%2A1%5E2=+x%5E2++-4 ALIGN=MIDDLE  ALT=\"2%28y%5E2-2y%2B1%5E2%29-2%2A1%5E2=+x%5E2++-4\"   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=2%28y-1%29%5E2-2=+x%5E2++-4 ALIGN=MIDDLE  ALT=\"2%28y-1%29%5E2-2=+x%5E2++-4\"   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=2%28y-1%29%5E2=+x%5E2++-4%2B2 ALIGN=MIDDLE  ALT=\"2%28y-1%29%5E2=+x%5E2++-4%2B2\"   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=%28y-1%29%5E2=+%28x%5E2++-2%29%2F2 ALIGN=MIDDLE  ALT=\"%28y-1%29%5E2=+%28x%5E2++-2%29%2F2\"   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=y=+sqrt%28x%5E2%2F2++-1%29%2B1 ALIGN=MIDDLE  ALT=\"y=+sqrt%28x%5E2%2F2++-1%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>hyperbola\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing+%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%280%2C2%2C.12%29%2Clocate%280%2C2%2Cp%280%2C2%29%29%2C%0D%0Agraph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+sqrt%28x%5E2%2F2++-1%29%2B1%2C+-sqrt%28x%5E2%2F2++-1%29%2B1%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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