document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=142614>Question 142614</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The radius of a circle defined by x^2+y^2-2x-4y+1=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103806 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=103806\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The standard equation for a circle with radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > and center at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<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=%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So, you have to complete the square for x and for y in your equation to put it into standard form.  That way you can determine the radius directly.\r<BR>\n" );
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document.write( "Process:<BR>\n" );
document.write( "Step 1:  Rearrange the equation so that the constant is on the right and the variables are grouped on the left:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x%2By%5E2-4y=-1 ALIGN=MIDDLE  ALT=\"x%5E2-2x%2By%5E2-4y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 2:  Take the coefficient on the 1st degree x term, divide by 2 and square the result.  Add that result to both sides of the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-2%29%2F2%29%5E2=1 ALIGN=MIDDLE  ALT=\"%28%28-2%29%2F2%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > so  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x%2B1%2By%5E2-4y=-1%2B1 ALIGN=MIDDLE  ALT=\"x%5E2-2x%2B1%2By%5E2-4y=-1%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 3:  Repeat step 2 for the 1st degree y term.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-4%29%2F2%29%5E2=4 ALIGN=MIDDLE  ALT=\"%28%28-4%29%2F2%29%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x%2B1%2By%5E2-4y%2B4=-1%2B1%2B4 ALIGN=MIDDLE  ALT=\"x%5E2-2x%2B1%2By%5E2-4y%2B4=-1%2B1%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 4:  Factor the two trinomial parts of the left and collect terms on the right.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x%2B1=%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-2x%2B1=%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-4y%2B4=%28y-2%29%5E2 ALIGN=MIDDLE  ALT=\"y%5E2-4y%2B4=%28y-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2%2B%28y-2%29%5E2=4 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2%2B%28y-2%29%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 5: Take the square root of the resulting constant term to find the radius\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29=2 ALIGN=MIDDLE  ALT=\"sqrt%284%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Super-Double-Plus Extra Credit:  Write the ordered pair that represents the center of this circle.\r<BR>\n" );
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