document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=990644>Question 990644</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the circle whose centre lies on the line x = 2y, passes throught the point (2,5), and for which the lenght of the tangent from the origin is sqrt{ 7)}}. 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 #612443 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=612443\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since centre lies on x=2y,<BR>\n" );
document.write( "Let the centre be (2a,a)<BR>\n" );
document.write( "Eqn of circle will be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2a%29%5E2+%2B+%28y-a%29%5E2+=+r%5E2 ALIGN=MIDDLE  ALT=\"%28x-2a%29%5E2+%2B+%28y-a%29%5E2+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since it passes through (2,5), putting it we get,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282-2a%29%5E2+%2B+%285-a%29%5E2+=+r%5E2 ALIGN=MIDDLE  ALT=\"%282-2a%29%5E2+%2B+%285-a%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=4a%5E2-8a%2B4+%2B+a%5E2-10a%2B25+=+r%5E2 ALIGN=MIDDLE  ALT=\"4a%5E2-8a%2B4+%2B+a%5E2-10a%2B25+=+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=5a%5E2-18a%2B29+=+r%5E2 ALIGN=MIDDLE  ALT=\"5a%5E2-18a%2B29+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >----------------------------------------(i)<BR>\n" );
document.write( "Now length of tangent from origin is sqrt(7)<BR>\n" );
document.write( "So, using pythagoras theorem,<BR>\n" );
document.write( " (Distance of centre from origin)^2 = (length of tangent)^2 + (radius)^2<BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282a-0%29%5E2%2B+%28a-0%29%5E2+=+7+%2B+r%5E2 ALIGN=MIDDLE  ALT=\"%282a-0%29%5E2%2B+%28a-0%29%5E2+=+7+%2B+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=5a%5E2-7+=+r%5E2 ALIGN=MIDDLE  ALT=\"5a%5E2-7+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----------------------------(ii)<BR>\n" );
document.write( "Subtracting (i) from (ii),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18a-36+=+0 ALIGN=MIDDLE  ALT=\"18a-36+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Putting back in eqn (ii),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=13 ALIGN=MIDDLE  ALT=\"r%5E2=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Putting both values in eqn of circle we get,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2+%2B+%28y-2%29%5E2+=+13 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2+%2B+%28y-2%29%5E2+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x%2By%5E2-4y%2B7=0 ALIGN=MIDDLE  ALT=\"x%5E2-8x%2By%5E2-4y%2B7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "P.S. - \"The Elements of Coordinate Geometry\" by S. L. Loney </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );