document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=936629>Question 936629</A>: <I><SPAN STYLE=\"word-break: break-all;\"> .Find the equation of the smaller circle that is tangent to the axes and the circle x^2+y^2=2x+2y-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #570088 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=570088\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First find the equation of the circle by completing the square in x and y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x%2By%5E2-2y=-1 ALIGN=MIDDLE  ALT=\"x%5E2-2x%2By%5E2-2y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-2x%2B1%29%2B%28y%5E2-2y%2B1%29=-1%2B1%2B1 ALIGN=MIDDLE  ALT=\"%28x%5E2-2x%2B1%29%2B%28y%5E2-2y%2B1%29=-1%2B1%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2%2B%28y-1%29%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2%2B%28y-1%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The circle is centered at (1,1) and has a radius of 1.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C5%2C-2%2C5%2Cgreen%28line%281.464%2C1.464%2C5%2C5%29%29%2Cblue%28line%280%2C.89%2C.89%2C.89%29%29%2Cblue%28line%280.89%2C.89%2C1.464%2C1.464%29%29%2Cline%280%2C0%2C0%2C10%29%2Cline%280%2C0%2C10%2C0%29%2Clocate%280.3%2C0.9%2Cr%29%2Clocate%281.2%2C1.3%2Cr%29%2Ccircle%281.49%2C1.49%2C0.1%29%2Ccircle%280.89%2C.89%2C.89%29%2Clocate%283%2C3%2CR=1%29%2C%28circle%285%2C5%2C5%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The point of intersection of the large circle and the small circle is shown in the diagram. <BR>\n" );
document.write( "The coordinates of the position are given by,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y=1-1%28sqrt%282%29%2F2%29%29=1-sqrt%282%29%2F2%29%29 ALIGN=MIDDLE  ALT=\"x=y=1-1%28sqrt%282%29%2F2%29%29=1-sqrt%282%29%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or approximately (0.2929,0.2929).<BR>\n" );
document.write( "That distance is equal to,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2B%28sqrt%282%29%2F2%29r=1-sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"r%2B%28sqrt%282%29%2F2%29r=1-sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%281-sqrt%282%29%2F2%29%2F%281%2Bsqrt%282%29%2F2%29 ALIGN=MIDDLE  ALT=\"r=%281-sqrt%282%29%2F2%29%2F%281%2Bsqrt%282%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0.1715 ALIGN=MIDDLE  ALT=\"r=0.1715\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the smaller circle is centered at (0.1715,0.1715) and has a radius of 0.1715.<BR>\n" );
document.write( "So the equation would be,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-0.1715%29%5E2%2B%28y-0.1715%29%5E2=0.1715%5E2 ALIGN=MIDDLE  ALT=\"%28x-0.1715%29%5E2%2B%28y-0.1715%29%5E2=0.1715%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%28%28x-0.1715%29%5E2%2B%28y-0.1715%29%5E2=0.0294%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x-0.1715%29%5E2%2B%28y-0.1715%29%5E2=0.0294%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );