document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969255>Question 969255</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of the circle satisfying the given condition.<BR>\n" );
document.write( "Radius of  2<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+5+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, tangent to y=2x and passing through (3,-4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592191 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=592191\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write the equation of the circle satisfying the given condition.<BR>\n" );
document.write( "Radius of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%285%29 ALIGN=MIDDLE  ALT=\"2sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, tangent to y = 2x and passing through (3,-4)<BR>\n" );
document.write( "===============<BR>\n" );
document.write( "The center has to be on the line parallel to y = 2x and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%285%29+=+sqrt%2820%29 ALIGN=MIDDLE  ALT=\"2sqrt%285%29+=+sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > units from the line.<BR>\n" );
document.write( "Find the line's equation:<BR>\n" );
document.write( "y = 2x has a slope of 2 and passes thru (0,0)<BR>\n" );
document.write( "A line perpendicular to it (RS) thru (0,0) is y = -x/2<BR>\n" );
document.write( "A point on the line RS sqrt(20) from (0,0) is the intersection of a circle centered at (0,0) with r = sqrt(20) <BR>\n" );
document.write( "--> x^2 + y^2 = 20<BR>\n" );
document.write( "y = -x/2<BR>\n" );
document.write( "x^2 + x^2/4 = 20<BR>\n" );
document.write( "x = 4  (Ignore the x = -4 in Q2, (3,-4) is in Q4)<BR>\n" );
document.write( "--> (4,-2)<BR>\n" );
document.write( "The center of the circle is on a line thru (4,-2) with m = 2 (parallel to y = 2x)<BR>\n" );
document.write( "y+2 = 2(x-4) = 2x - 8<BR>\n" );
document.write( "y = 2x - 10<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Find the point(s) sqrt(20) from (3,-4) on the line y = 2x - 10<BR>\n" );
document.write( "It's the intersections of a circle centered at (3,-4) r = sqrt(20)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3%29%5E2+%2B+%28y%2B4%29%5E2+=+20 ALIGN=MIDDLE  ALT=\"x-3%29%5E2+%2B+%28y%2B4%29%5E2+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sub for y<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2+%2B+%282x-6%29%5E2+=+20 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2+%2B+%282x-6%29%5E2+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2+%2B+4%28x-3%29%5E2+=+20 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2+%2B+4%28x-3%29%5E2+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2+=+4 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 5 --> center @ (5,0) --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2+%2B+y%5E2+=+20 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2+%2B+y%5E2+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ** Circle #1<BR>\n" );
document.write( "----<BR>\n" );
document.write( "x = 1 --> center @ (1,-8) --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2+%2B+%28y%2B8%29%5E2+=+20 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2+%2B+%28y%2B8%29%5E2+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ** Circle #2<BR>\n" );
document.write( "=============================<BR>\n" );
document.write( "There must be an easier way to do this, but I don't know of one. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );