document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139523>Question 1139523</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The circle is tangent to the line 5x+y=3 at the point (2,-7) and center is on the line x-2y=19. Find the equation of the circle. (I'm struggling to find the center in x-2y=19 that says to be perpendicular to the center itself and to the point of tangency)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #759993 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=759993\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "A radius of a circle to a point of tangency is perpendicular to the tangent at that point.<br><BR>\n" );
document.write( "You are given a point of tangency (2,-7) and the equation of the tangent at that point.  So you know the center of the circle is somewhere on the line that is perpendicular to the tangent at (2,-7); find the equation of that line.<br><BR>\n" );
document.write( "You are also given the equation of another line that the center of the circle lies on.<br><BR>\n" );
document.write( "You have equations for two lines that both contain the center of the circle.  Solve the pair of equations to find the center of the circle.<br><BR>\n" );
document.write( "Then use the distance formula to find the radius of the circle (distance between the center and (2,-7)).<br><BR>\n" );
document.write( "Then plug the numbers into the standard form for the equation of a circle.<BR>\n" );
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