SOLUTION: Find an equation of the line tangent to the circle (x − 9)^2 + (y − 2)^2 = 25 at the point (12, −2)

Algebra ->  Linear-equations -> SOLUTION: Find an equation of the line tangent to the circle (x − 9)^2 + (y − 2)^2 = 25 at the point (12, −2)      Log On


   

Question 310361: Find an equation of the line tangent to the circle (x − 9)^2 + (y − 2)^2 = 25 at the point (12, −2)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's use implicit differentiation to find the derivative at that point.
%28x-9%29%5E2%2B%28y-2%29%5E2=25
Differentiating,
2%28x-9%29dx%2B2%28y-2%29dy=0
%28y-2%29dy=%289-x%29dx
dy%2Fdx=%289-x%29%2F%28y-2%29
The value of the derivative equals the slope of the tangent line at that point.
So at (12,-2),
dy%2Fdx=%289-12%29%2F%28-2-2%29
dy%2Fdx=-3%2F-4=3%2F4
Use the point-slope form of a line,
y-yp=m%28x-xp%29
y-%28-2%29=%283%2F4%29%28x-12%29
y%2B2=%283%2F4%29x-9
y=%283%2F4%29x-11