SOLUTION: the equation of a tangent line to the curve x^2+y^2=169 at the point (5,-12) is?

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Question 266674: the equation of a tangent line to the curve x^2+y^2=169 at the point (5,-12) is?
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
step 1 - we take a derivative of both sides and get
2x+%2B+2y%28dy%2Fdx%29+=+0
step 2 - solve for dy/dx
%28dy%2Fdx%29+=+-x%2Fy
step 3 - put your coordinates in and get
%28dy%2Fdx%29+=+-5%2F-12
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so, the slope is
dy/dx = m = 5/12
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step 4 - using slope and our coordinate as well as y = mx + b, we get
y+=+mx+%2B+b
and then
-12+=+%285%2F12%29%2A5+%2B+b
solving for b, we get
-169%2F12+=+b
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step 5 - final equation is
y+=+%285%2F12%29x+-+169%2F12