document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=906935>Question 906935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the length of the tangent (-4,1) on the circle given by the equation x^2+y^2+8x+12y+5=0. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #550102 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=550102\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find the length of the tangent (-4,1) on the circle given by the equation x^2+y^2+8x+12y+5=0.<BR>\n" );
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document.write( "Find the center of the circle.<BR>\n" );
document.write( "Put the equation is standard form.<BR>\n" );
document.write( "(x+4)^2 + (y+6)^2 = 47<BR>\n" );
document.write( "--> center at (-4,-6)<BR>\n" );
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document.write( "Move the circle and the point 6 units up and 4 units right.<BR>\n" );
document.write( "Now the circle is x^2 + y^2 = 47 and the point is (0,7)<BR>\n" );
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document.write( "Find the tangent that passes thru (0,7)<BR>\n" );
document.write( "(x,y) is a point on the circle<BR>\n" );
document.write( "The slope of the tangent m1 = (y-7)/x<BR>\n" );
document.write( "The slope of the tangent at any point on the circle m2 = -x/y<BR>\n" );
document.write( "m1 = m2<BR>\n" );
document.write( "(y-7)/x = -x/y<BR>\n" );
document.write( "-x^2 = y^2 - 7y<BR>\n" );
document.write( "x^2 + y^2 = 7y<BR>\n" );
document.write( "x^2 + y^2 = 47<BR>\n" );
document.write( "7y = 47<BR>\n" );
document.write( "y = 47/7<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%2847+-+47%5E2%2F7%5E2%29+=+sqrt%2894%29%2F7 ALIGN=MIDDLE  ALT=\"x+=+sqrt%2847+-+47%5E2%2F7%5E2%29+=+sqrt%2894%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "One tangent point is (sqrt(94)/7,(47/7))<BR>\n" );
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document.write( "Find the distance between those 2 points. </SPAN>\n" );
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