document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=827899>Question 827899</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find he 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( "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 #498942 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=498942\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find he 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<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Find the standard eqn of the circle.<BR>\n" );
document.write( "x^2 + y^2 - 2x + 8y - 23 = 0<BR>\n" );
document.write( "(x-1)^2 + (y+4)^2 = 40<BR>\n" );
document.write( "Its center is (1,-4) and radius sqrt(40)<BR>\n" );
document.write( "------<BR>\n" );
document.write( "a) at the point (3,-10) on it<BR>\n" );
document.write( "Use  a circle about the Origin with radius sqrt(40)<BR>\n" );
document.write( "--> x^2 + y^2 = 40<BR>\n" );
document.write( "The tangent and any point is -x/y<BR>\n" );
document.write( "Point (3,-10) is translated to (2,-6)<BR>\n" );
document.write( "Slope = 1/3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Eqn of a line thru (3,-10) with a slope of 3 is<BR>\n" );
document.write( "y+10 = (1/3)*(x-3)<BR>\n" );
document.write( "=====================================<BR>\n" );
document.write( "b) having slope of 3<BR>\n" );
document.write( "Using the circle about the Origin:<BR>\n" );
document.write( "-x/y = 3<BR>\n" );
document.write( "x^2 + y^2 = 40<BR>\n" );
document.write( "x = -3y<BR>\n" );
document.write( "9y^2 + y^2 = 40<BR>\n" );
document.write( "y = -2, +2<BR>\n" );
document.write( "--> (6,-2)<BR>\n" );
document.write( "Translated to the given circle:<BR>\n" );
document.write( "--> (7,-6)<BR>\n" );
document.write( "y+6 = 3(x-7)<BR>\n" );
document.write( "=======================<BR>\n" );
document.write( "--> (-6,2)<BR>\n" );
document.write( "Translate to the given circle<BR>\n" );
document.write( "--> (-5,-2)<BR>\n" );
document.write( "y+2 = 3x+15<BR>\n" );
document.write( " </SPAN>\n" );
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