document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=653881>Question 653881</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the line satisfying the given conditions:<BR>\n" );
document.write( "Is tangent to the circle 2x^2+2y^2-12x+16y=0 at the point (6,-8) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #408538 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=408538\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Complete the square for both variables in your equation for the circle:\r<BR>\n" );
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document.write( "1.  Divide by the lead coefficient\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ y^2\ -\ 6x\ +\ 8y\ =\ 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 6x\ +\ 9\ +\ y^2\ +\ 8y\ +\ 16\ =\ 25\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x\ -\ 3)^2\ +\ (y\ +\ 4)^2\ =\ 25\">\r<BR>\n" );
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document.write( "Note that the center of the circle is at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (3, -4)\"> and that the radius is 5.\r<BR>\n" );
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document.write( "2.  Find the slope of the line containing the radius segment from the center of the circle to the point of tangency.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ m_r\ =\ \frac{y_1\ -\ y_2}{x_1\ -\ x_2}\ =\ \frac{-4\ -\ (-8)}{3\ -\ 6}\">\r<BR>\n" );
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document.write( "You do your own arithmetic\r<BR>\n" );
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document.write( "3.  Use the fact that any tangent to a circle is perpendicular to the radius at the point of tangency plus the fact that the slopes of perpendicular lines are negative reciprocals to calculate the slope of the desired line.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE m\ =\ -\frac{1}{m_r}\">\r<BR>\n" );
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document.write( "4.  Use the point-slope form of an equation of a line to derive the desired equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ y_1\ =\ m(x\ -\ x_1) \">\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_1,y_1\right)\"> are the coordinates of the given point and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large m\"> is the slope calculated in step 3. \r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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