SOLUTION: Write the equation of the tangent line to (x-2)�+(y+2)�=169 at the point (7,10). Please answer as soon as possible. I have a test tomorrow and my teacher has not given enough ti

Question 923109: Write the equation of the tangent line to (x-2)�+(y+2)�=169 at the point (7,10).
Please answer as soon as possible. I have a test tomorrow and my teacher has not given enough time into teaching us this! Please help! I need to know all the steps and how to get it. I know that it does include y=mx+b and I think the distance and midpoint formulas though.
Found 2 solutions by josgarithmetic, lwsshak3:
Answer by josgarithmetic(39621) (Show Source): You can put this solution on YOUR website!
Find derivative and then evaluate the derivative at the point (7,10).

What is the value of this rate of change at the given point?

.
That is a slope.

You are more completely looking for , and you know x and y from the given point, but you do not yet know b.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Write the equation of the tangent line to (x-2)�+(y+2)�=169 at the point (7,10).
***
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.
..
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
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