document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=870460>Question 870460</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write the equation of this circle\r<BR>\n" );
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document.write( "the equation of the line tangent \r<BR>\n" );
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document.write( "x^2+y^2=225 at (9,-12)\r<BR>\n" );
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document.write( "please help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #524885 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=524885\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What you MEAN is, find the equation of the tangent line to the circle at the point (9,-12).\r<BR>\n" );
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document.write( "The circle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=225 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=225\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The center is (0,0) and the radius is sqrt(225) but not necessary to solve the problem.  The center point IS necessary.\r<BR>\n" );
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document.write( "Is the given point really on the circle?<BR>\n" );
document.write( "9*9+144=225?<BR>\n" );
document.write( "81+144=225, Yes.\r<BR>\n" );
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document.write( "The slope of the line containing (0,0) and (9,-12) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2F3 ALIGN=MIDDLE  ALT=\"-4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >; so the line perpendicular must have slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Note that (0,0) and (9,-12) forms a radius of the circle.\r<BR>\n" );
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document.write( "We want the line so that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%2F4%29x%2Bb ALIGN=MIDDLE  ALT=\"y=%283%2F4%29x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > and contains (9,-12).  We can find the value for b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=y-mx ALIGN=MIDDLE  ALT=\"b=y-mx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-12-%283%2F4%299 ALIGN=MIDDLE  ALT=\"b=-12-%283%2F4%299\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-12-27%2F4 ALIGN=MIDDLE  ALT=\"b=-12-27%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-48%2F4-27%2F4 ALIGN=MIDDLE  ALT=\"b=-48%2F4-27%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-75%2F4 ALIGN=MIDDLE  ALT=\"b=-75%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Equation:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=%283%2F4%29x-75%2F4%29 ALIGN=MIDDLE  ALT=\"highlight%28y=%283%2F4%29x-75%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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