SOLUTION: write the equation of the line tangent to the circle x^2 +y^2=169 at the point (-5,12)

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Question 1041658: write the equation of the line tangent to the circle x^2 +y^2=169 at the point (-5,12)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
That point is in quadrant four and the center of the circle is the Origin. Find the derivative of y AT THAT POINT (-5,12), and that will be the slope.

%28dy%2Fdx%29%28x%5E2%2By%5E2%29=%28dy%2Fdx%29%28169%29
2x%2B2y%28dy%2Fdx%29=0
2y%28dy%2Fdx%29=-2x
dy%2Fdx=-2x%2F%282y%29
dy%2Fdx=-x%2Fy, which can be assigned m.

slope m=-%28-5%29%2F%2812%29
m=5%2F12

POINT-SLOPE EQUATION FORM: y-12=%285%2F12%29%28x-%28-5%29%29
y=%285%2F12%29x%2B25%2F12%2B12
y=%285%2F12%29x%2B%2825%2B144%29%2F12
highlight%28y=%285%2F12%29x%2B169%2F12%29-----the tangent line, in SLOPE-INTERCEPT FORM