document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166904>Question 1166904</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Calculate the length of a tangent to the circle: x^2+y^2+8x−2y−8=0 at its point of tangency from the point P(2,4) which is off the circle. Make sure to show your work. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #791484 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=791484\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rewrite and the equation of the circle is x^2+8x+y^2-2y=8<BR>\n" );
document.write( "complete both squares and x^2+8x+16+y^2-2y+1=25<BR>\n" );
document.write( "this is (x+4)^2+(y-1)^2=5^2<BR>\n" );
document.write( "circle with center at (-4, 1) and radius 5<BR>\n" );
document.write( "The tangent line is perpendicular to the radius of the circle, which is 5 units.<BR>\n" );
document.write( "The distance between the center of the circle and the point is sqrt (36+9)=sqrt (45) units, using the distance formula.  That is the hypotenuse of the triangle.  The third leg is the distance from the point to the circle, and that is D^2+5^2=sqrt(45)^2<BR>\n" );
document.write( "or d^2=20<BR>\n" );
document.write( "d=2 sqrt (5) units.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );