document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=971063>Question 971063</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Two circles have their centres on the line y+3=0 and touch the line 3y-2x=0. If the radii of circles are  \sqrt{13}  <BR>\n" );
document.write( "Find the equations of the circle and the coordinates of their centres <BR>\n" );
document.write( "Hint use similar triangles. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593887 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=593887\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since centres of circles lie on y+3=0, i.e y= -3<BR>\n" );
document.write( "Let coordinates of centres be (x,-3)<BR>\n" );
document.write( "Since the circles touch the line -2x+3y=0<BR>\n" );
document.write( "So, the distance from centre of circles to this line are radii of circles.<BR>\n" );
document.write( "So, Using the distance formula i.e \r<BR>\n" );
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document.write( "(|-2x+3*(-3)|)/(sqrt((-2^2)+3^2)) = sqrt(13)  (|..| = mod sign)<BR>\n" );
document.write( "or, |-2x+3*(-3)| = 13<BR>\n" );
document.write( "or, -2x-9 = (+-13)<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x-9+=+13 ALIGN=MIDDLE  ALT=\"-2x-9+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" > -(i) or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x-9+=+-13 ALIGN=MIDDLE  ALT=\"-2x-9+=+-13\"   DISABLED_style= \"max-width:90%; height:auto;\" >- (ii)<BR>\n" );
document.write( "Solving both eqns. separately,<BR>\n" );
document.write( "we get, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+-11 ALIGN=MIDDLE  ALT=\"x=+-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the coordinates of center are (-11,-3) and (2,-3)<BR>\n" );
document.write( "Equations of circles are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B11%29%5E2+%2B+%28y%2B3%29%5E2+=+13 ALIGN=MIDDLE  ALT=\"%28x%2B11%29%5E2+%2B+%28y%2B3%29%5E2+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2+%2B+%28y%2B3%29%5E2+=+13 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2+%2B+%28y%2B3%29%5E2+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "i.e. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+%2B+22x+%2B+6y+-117+=0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+%2B+22x+%2B+6y+-117+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+-+4x+%2B+6y+=0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+-+4x+%2B+6y+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );