document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=828173>Question 828173</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Find the equation of all tangents to the circle x^2 + y^2 - 2x + 8y - 23 = 0<BR>\n" );
document.write( "a) at the point (3,-10) on it <BR>\n" );
document.write( "b) having slope of 3 \r<BR>\n" );
document.write( "\n" );
document.write( "Can you please help me out? Thanks so much in advance:) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #499088 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=499088\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the equation of all tangents to the circle <BR>\n" );
document.write( "x^2 + y^2 - 2x + 8y - 23 = 0<BR>\n" );
document.write( "Derivative: 2x + 2yy' - 2 + 8y' = 0<BR>\n" );
document.write( "y'(2y+8) = -2x+2<BR>\n" );
document.write( "----<BR>\n" );
document.write( "y' = (-2(x+1))/(2(y+4))<BR>\n" );
document.write( "y' = -(x+1)/(y+4)<BR>\n" );
document.write( "-----------\r<BR>\n" );
document.write( "\n" );
document.write( "a) at the point (3,-10) on it<BR>\n" );
document.write( "y'(3,-10) = -(3+1)/(-10+4) = -4/-6 = 2/3<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Form: y = mx + b<BR>\n" );
document.write( "-10 = (2/3)*3 + b<BR>\n" );
document.write( "-10 = 2 + b<BR>\n" );
document.write( "b = -12<BR>\n" );
document.write( "Tangent Equation:<BR>\n" );
document.write( "y = (2/3)x - 12<BR>\n" );
document.write( "========================== <BR>\n" );
document.write( "b) having slope of 3<BR>\n" );
document.write( "(-(x+1))/(y+4) = 3<BR>\n" );
document.write( "-x+1 = 3y+12<BR>\n" );
document.write( "3y = -x-11<BR>\n" );
document.write( "y = -(1/3)(x+1) <BR>\n" );
document.write( "===================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=====================<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );