document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=139830>Question 139830</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the radius of the circle 2x^2+2y^2-8x+16y-32=0? I think it is 6??????? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101924 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=101924\">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=2x%5E2%2B2y%5E2-8x%2B16y-32=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B2y%5E2-8x%2B16y-32=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-8x%2B2y%5E2%2B16y-32=0 ALIGN=MIDDLE  ALT=\"2x%5E2-8x%2B2y%5E2%2B16y-32=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-8x%2B2y%5E2%2B16y=%2B32 ALIGN=MIDDLE  ALT=\"2x%5E2-8x%2B2y%5E2%2B16y=%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32 ALIGN=MIDDLE  ALT=\"32\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-2%29%5E2-8%2B2y%5E2%2B16y=%2B32 ALIGN=MIDDLE  ALT=\"2%28x-2%29%5E2-8%2B2y%5E2%2B16y=%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" > Complete the square for the x terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-2%29%5E2-8%2B2%28y%2B4%29%5E2-32=%2B32 ALIGN=MIDDLE  ALT=\"2%28x-2%29%5E2-8%2B2%28y%2B4%29%5E2-32=%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" > Complete the square for the y terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-2%29%5E2%2B2%28y%2B4%29%5E2-40=%2B32 ALIGN=MIDDLE  ALT=\"2%28x-2%29%5E2%2B2%28y%2B4%29%5E2-40=%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-2%29%5E2%2B2%28y%2B4%29%5E2=%2B32%2B40 ALIGN=MIDDLE  ALT=\"2%28x-2%29%5E2%2B2%28y%2B4%29%5E2=%2B32%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40 ALIGN=MIDDLE  ALT=\"40\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-2%29%5E2%2B2%28y%2B4%29%5E2=72 ALIGN=MIDDLE  ALT=\"2%28x-2%29%5E2%2B2%28y%2B4%29%5E2=72\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28%28x-2%29%5E2%2B%28y%2B4%29%5E2%29=72 ALIGN=MIDDLE  ALT=\"2%28%28x-2%29%5E2%2B%28y%2B4%29%5E2%29=72\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the common term 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2B%28y%2B4%29%5E2=36 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2B%28y%2B4%29%5E2=36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-----------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice how the equation is now in the form <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;\" >. This means that this conic section is a circle where (h,k) is the center and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the radius.\r<BR>\n" );
document.write( "\n" );
document.write( "So the circle has these properties:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Center: (2,-4)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Radius: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=sqrt%2836%29=6 ALIGN=MIDDLE  ALT=\"r=sqrt%2836%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the radius of the circle is 6 units\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );