Question 923109
Write the equation of the tangent line to (x-2)²+(y+2)²=169 at the point (7,10).
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Given equation is that of a circle with center at (2,-2) and radius=√169=13
The tangent line through the point of tangency(7,10) is perpendicular to a 2nd  line through the same point of tangency and center of the circle (2,-2). Therefore, the slope of the tangent line is the negative reciprocal of this 2nd line.
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slope of 2nd line=∆y/∆x=(10-(-2))/(7-2)=12/5
slope of tangent line=-5/12
equation of tangent line: y=-5x/12+b
solve for b using coordinates of the point(7,10)on the line
10=-5*7/12+b
b=10+35/12=155/12
equation of tangent line: y=-5x/12+155/12