document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=272074>Question 272074</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation for the line tangent to the circle x^2+y^2=58 at the points (-3,7)\r<BR>\n" );
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document.write( "I dont even know where to begin this problem. thanks for the help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #199074 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=199074\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the equation for the line tangent to the circle x^2+y^2=58 at the points <BR>\n" );
document.write( "(-3,7) <BR>\n" );
document.write( "I dont even know where to begin this problem. thanks for the help.<BR>\n" );
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document.write( "The circle is the result of graphing two function:<BR>\n" );
document.write( "y = sqrt(58-x^2) <BR>\n" );
document.write( "and<BR>\n" );
document.write( "y = -sqrt(58-x^2)<BR>\n" );
document.write( "====================<BR>\n" );
document.write( "The 1st is in the 1st and 2nd quadrants.<BR>\n" );
document.write( "The 2nd is in the 3rd and 4th quadrants.<BR>\n" );
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document.write( "The point (-3,7) is in the 2nd quadrant so the tangency point <BR>\n" );
document.write( "is with y = sqrt(58-x^2)<BR>\n" );
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document.write( "Take the derivative of y = sqrt(58 - x^2)<BR>\n" );
document.write( "y' = (1/2)(58-x^2)^(-1/2)[-2x]<BR>\n" );
document.write( "y'= (-x)/sqrt(58-x^2)<BR>\n" );
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document.write( "Find the slope when x = -3<BR>\n" );
document.write( "y'(-3) = 3sqrt(49) = 21<BR>\n" );
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document.write( "Find the equation of the line with m = 21 passing thru (-3,7)<BR>\n" );
document.write( "7 = 21(-3)+b<BR>\n" );
document.write( "b = 70<BR>\n" );
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document.write( "Tangent Equation:<BR>\n" );
document.write( "y = 21x + 70<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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