document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=990645>Question 990645</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are two circles which passes through the point (1,2) and also touch both axes.Find the equation of the two possible circles.?! Please recomend any coordinate geometory textbook for me </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #612440 by </B><A HREF=/tutors/aboutme.mpl?userid=anand429><B>anand429(138)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=anand429><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=anand429><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=612440\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since the circle touches both the axes,<BR>\n" );
document.write( "we, can take center of circle as (r,r) where r is also radius of circle.<BR>\n" );
document.write( "(Draw a fig. to see clearly)<BR>\n" );
document.write( "So, equation of circle can be given by,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-r%29%5E2+%2B+%28y-r%29%5E2+=+r%5E2 ALIGN=MIDDLE  ALT=\"%28x-r%29%5E2+%2B+%28y-r%29%5E2+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --------------(i)<BR>\n" );
document.write( "Since, it passes through (1,2),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-r%29%5E2+%2B+%282-r%29%5E2+=+r%5E2 ALIGN=MIDDLE  ALT=\"%281-r%29%5E2+%2B+%282-r%29%5E2+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5E2-2r%2B1+%2B+r%5E2-4r%2B4+=+r%5E2 ALIGN=MIDDLE  ALT=\"+r%5E2-2r%2B1+%2B+r%5E2-4r%2B4+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2-6r%2B5+=+0 ALIGN=MIDDLE  ALT=\"r%5E2-6r%2B5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r-1%29%28r-5%29+=+0 ALIGN=MIDDLE  ALT=\"%28r-1%29%28r-5%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So r = 1 or r =5<BR>\n" );
document.write( "So, clearly we have two circles with centres at (1,1) and (5,5) with radii 1 and 5 respectively.<BR>\n" );
document.write( "Equation of circles be given by putting value of r in eqn (i):- <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%5E2 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2+%2B+%28y-1%29%5E2+=+1%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2+%2B+%28y-5%29%5E2+=+5%5E2 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2+%2B+%28y-5%29%5E2+=+5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(Simplify it.)\r<BR>\n" );
document.write( "\n" );
document.write( "A good coordinate geometry book:- \"The Elements of Coordinate geometry\" by S. L. Loney </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );