document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103514>Question 103514</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the center and radius of each circle and sketch graph: x^2-10x+y^2+8y=-10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75323 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=75323\">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=x%5E2-10x%2By%5E2%2B8y=-10 ALIGN=MIDDLE  ALT=\"x%5E2-10x%2By%5E2%2B8y=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The quickest way is to complete the square for both x and y. Then compare your equation to the equation of a circle and pick off the center of the circle and the radius. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-10x%2BA%29=x%5E2%2B2B%2BB%5E2=%28x%2BB%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E2-10x%2BA%29=x%5E2%2B2B%2BB%5E2=%28x%2BB%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Completing the square for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2%2B8y%2BC%29=x%5E2%2B2D%2BD%5E2=%28x%2BD%29%5E2 ALIGN=MIDDLE  ALT=\"%28y%5E2%2B8y%2BC%29=x%5E2%2B2D%2BD%5E2=%28x%2BD%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >Completing the square for y.<BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2B=-10 ALIGN=MIDDLE  ALT=\"2B=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=B%5E2 ALIGN=MIDDLE  ALT=\"A=B%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2D=8 ALIGN=MIDDLE  ALT=\"2D=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=D%5E2 ALIGN=MIDDLE  ALT=\"C=D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's solve for B and A.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2B=-10 ALIGN=MIDDLE  ALT=\"2B=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28B=-5%29 ALIGN=MIDDLE  ALT=\"highlight%28B=-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=B%5E2 ALIGN=MIDDLE  ALT=\"A=B%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A=25%29 ALIGN=MIDDLE  ALT=\"highlight%28A=25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's solve for D and C.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2D=8 ALIGN=MIDDLE  ALT=\"2D=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28D=4%29 ALIGN=MIDDLE  ALT=\"highlight%28D=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=D%5E2 ALIGN=MIDDLE  ALT=\"C=D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28C=16%29 ALIGN=MIDDLE  ALT=\"highlight%28C=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-10x%2By%5E2%2B8y=-10 ALIGN=MIDDLE  ALT=\"x%5E2-10x%2By%5E2%2B8y=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-10x%2BA%29%2B%28y%5E2%2B8y%2BC%29=-10%2BA%2BC ALIGN=MIDDLE  ALT=\"%28x%5E2-10x%2BA%29%2B%28y%5E2%2B8y%2BC%29=-10%2BA%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add A and C to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2BB%29%5E2%2B%28y%2BD%29%5E2=-10%2BA%2BC ALIGN=MIDDLE  ALT=\"%28x%2BB%29%5E2%2B%28y%2BD%29%5E2=-10%2BA%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" >Substitute with the completed squares from above.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2%2B%28y%2B4%29%5E2=-10%2B25%2B16 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2%2B%28y%2B4%29%5E2=-10%2B25%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" >Substitute your calculated values for A,B,C,D.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2%2B%28y%2B4%29%5E2=-10%2B25%2B16 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2%2B%28y%2B4%29%5E2=-10%2B25%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2%2B%28y%2B4%29%5E2=31 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2%2B%28y%2B4%29%5E2=31\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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;\" > The equation of a circle centered at (h,k) with a radius R.<BR>\n" );
document.write( "In this case, <BR>\n" );
document.write( "(h,k)=(5,-4) and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2=31 ALIGN=MIDDLE  ALT=\"R%5E2=31\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=sqrt%2831%29 ALIGN=MIDDLE  ALT=\"R=sqrt%2831%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-2%2C+12%2C+-12%2C+2%2Cgrid%28+1+%29%2Cblue%28circle%28+5%2C+-4%2C+.2+%29%29%2Cgreen%28circle%28+5%2C+-4%2C+5.567+%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );