document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=480006>Question 480006</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the circle passes through the points (0, 0), (O, 5), (3, 3). Find the equation of the circle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #328833 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=328833\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The circle passes through the points (0, 0), (O, 5), (3, 3). Find the equation of the circle.<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Standard form of equation for circle: (x-h)^2+(y-k)^2=r^2, (h,k) being the center of the circle with radius=r.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "3 equations from coordinates of given 3 points (0, 0), (0, 5), (3,3)<BR>\n" );
document.write( "1) (0-h)^2+(0-k)^2=r^2<BR>\n" );
document.write( "2) (0-h)^2+(5-k)^2=r^2<BR>\n" );
document.write( "3) (3-h)^2+(3-k)^2=r^2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "solving for k<BR>\n" );
document.write( "1) (0-h)^2+(0-k)^2=r^2<BR>\n" );
document.write( "2) (0-h)^2+(5-k)^2=r^2<BR>\n" );
document.write( "subtract eq2 fm eq1<BR>\n" );
document.write( "k^2-(5-k)^2=0<BR>\n" );
document.write( "k^2-(25-10k+k^2)=0<BR>\n" );
document.write( "k^2-25+10k-k^2=0<BR>\n" );
document.write( "25-10k=0<BR>\n" );
document.write( "10k=25<BR>\n" );
document.write( "k=2.5 or 5/2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "solving for h<BR>\n" );
document.write( "2) (0-h)^2+(5-k)^2=r^2<BR>\n" );
document.write( "3) (3-h)^2+(3-k)^2=r^2<BR>\n" );
document.write( "subtract eq3 fm eq2<BR>\n" );
document.write( "h^2+(5-2.5)^2-[(3-h)^2+(3-2.5)^2]=0<BR>\n" );
document.write( "h^2+(2.5)^2-[9-6h+h^2+.5^2]=0<BR>\n" );
document.write( "h^2+6.25-9+6h-h^2-.25=0<BR>\n" );
document.write( "6.25-9.25+6h=0<BR>\n" );
document.write( "-3=-6h<BR>\n" );
document.write( "h=.5 or 1/2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "solving for r<BR>\n" );
document.write( "1) (0-h)^2+(0-k)^2=r^2<BR>\n" );
document.write( "(1/2)^2+(5/2)^2=r^2<BR>\n" );
document.write( "1/4+25/4=r^2=26/4=13/2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation of circle:<BR>\n" );
document.write( "(x-1/2)^2+(y-5/2)^2=13/2<BR>\n" );
document.write( "see graph below as visual check on answer<BR>\n" );
document.write( "note: a more precise algebriac check can be made by plugging in coordinates of given points into equation<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=±(13/2-(x-.5)^2)^.5+2.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-6%2C+6%2C+-6%2C+6%2C+%2813%2F2-%28x-.5%29%5E2%29%5E.5%2B2.5%2C-%2813%2F2-%28x-.5%29%5E2%29%5E.5%2B2.5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );