SOLUTION: Find the equation of the tangent line to the curve (x-y)^2=2x+1 at the point (4,1).

Algebra ->  Graphs -> SOLUTION: Find the equation of the tangent line to the curve (x-y)^2=2x+1 at the point (4,1).      Log On


   

Question 1010151: Find the equation of the tangent line to the curve (x-y)^2=2x+1 at the point (4,1).
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-2xy%2By%5E2=2x%2B1
Differentiate implicitly.
2xdx-%282xdy%2B2ydx%29%2B2ydy=2dx
%28-2x%2B2y%29dy=%282y-2x%2B2%29dx
dy%2Fdx=%282y-2x%2B2%29%2F%282y-2x%29
dy%2Fdx=%28y-x%2B1%29%2F%28y-x%29
So at (4,1),
m=dy%2Fdx=%281-4%2B1%29%2F%281-4%29=%28-2%29%2F%28-3%29
m=2%2F3
So then,
y-1=%282%2F3%29%28x-4%29
y-1=%282%2F3%29x-8%2F3
y=%282%2F3%29x-8%2F3%2B3%2F3
highlight%28y=%282%2F3%29x-5%2F3%29
.