document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1144028>Question 1144028</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, i just need some help. Find the values of the constant k so that the graph of x^2+y^2+6x-4y=k^2-k-33 is a.) a circle, b.) a single point and c.) an empty set. I found a same problem but i need a whole solution thank you very much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #764987 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=764987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2B6x-4y=k%5E2-k-33 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2B6x-4y=k%5E2-k-33\"   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=%28x%5E2%2B6x%29%2B%28y%5E2-4y%29=k%5E2-k-33 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B6x%29%2B%28y%5E2-4y%29=k%5E2-k-33\"   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=%28x%5E2%2B6x%2B3%5E2%29-3%5E2%2B%28y%5E2-4y%2B2%5E2%29-2%5E2=k%5E2-k-33 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B6x%2B3%5E2%29-3%5E2%2B%28y%5E2-4y%2B2%5E2%29-2%5E2=k%5E2-k-33\"   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=%28x%2B3%29%5E2-9%2B%28y-2%29%5E2-4=k%5E2-k-33 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2-9%2B%28y-2%29%5E2-4=k%5E2-k-33\"   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=%28x%2B3%29%5E2%2B%28y-2%29%5E2-13=k%5E2-k-33 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2%2B%28y-2%29%5E2-13=k%5E2-k-33\"   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=%28x%2B3%29%5E2%2B%28y-2%29%5E2=k%5E2-k-33%2B13 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2%2B%28y-2%29%5E2=k%5E2-k-33%2B13\"   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=%28x%2B3%29%5E2%2B%28y-2%29%5E2=k%5E2-k-20 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2%2B%28y-2%29%5E2=k%5E2-k-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> it’s a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=circle ALIGN=MIDDLE  ALT=\"circle\"   DISABLED_style= \"max-width:90%; height:auto;\" > with center at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   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;\" >) and radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28k%5E2-k-20%29 ALIGN=MIDDLE  ALT=\"sqrt%28k%5E2-k-20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >: to have real solution find for what value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >} is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2-k-20=0+ ALIGN=MIDDLE  ALT=\"k%5E2-k-20=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=k%5E2-k-20=0 ALIGN=MIDDLE  ALT=\"k%5E2-k-20=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....factor completely\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2%2B4k-5k-20=0 ALIGN=MIDDLE  ALT=\"k%5E2%2B4k-5k-20=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=%28k%5E2%2B4k%29-%285k%2B20%29=0 ALIGN=MIDDLE  ALT=\"%28k%5E2%2B4k%29-%285k%2B20%29=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=k%28k%2B4%29-5%28k%2B4%29=0 ALIGN=MIDDLE  ALT=\"k%28k%2B4%29-5%28k%2B4%29=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=%28k-5%29%28k%2B4%29=0 ALIGN=MIDDLE  ALT=\"%28k-5%29%28k%2B4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=5 ALIGN=MIDDLE  ALT=\"k=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k=-4 ALIGN=MIDDLE  ALT=\"+k=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "using tese solution we will have radius equal to zero\r<BR>\n" );
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document.write( "then, the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2B6x-4y=k%5E2-k-33 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2B6x-4y=k%5E2-k-33\"   DISABLED_style= \"max-width:90%; height:auto;\" > is \r<BR>\n" );
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document.write( "a.) a circle\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3E5+ ALIGN=MIDDLE  ALT=\"k%3E5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3C-4 ALIGN=MIDDLE  ALT=\"k%3C-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+ ALIGN=MIDDLE  ALT=\"k+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is in interval: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "b.) a single point \r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=5 ALIGN=MIDDLE  ALT=\"k=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-4 ALIGN=MIDDLE  ALT=\"k=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c.) an empty set\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3C5 ALIGN=MIDDLE  ALT=\"k%3C5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3E-4 ALIGN=MIDDLE  ALT=\"k%3E-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+ ALIGN=MIDDLE  ALT=\"k+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%3Ck%3C5 ALIGN=MIDDLE  ALT=\"-4%3Ck%3C5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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