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

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


   

Question 389891: Find the equation of the tangent line to the curve x^2 +2xy-y^2 +x=2 at (1,2)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the equation of the tangent line
to the curve x^2 +2xy-y^2 +x=2 at (1,2)
----------------------
Derivative:
2x + 2[xy'+y]-2yy'+1= 0
---
Solve for y':
2x + 2xy' +2y - 2yy' + 1 =0
---
y'(2x-2y) = -[2x+2y+1]
---
y' = -[2x+2y+1]/[2x-2y]
---
Slope at (1,2) = -[2+4+1]/[2-4]
---
Slope at (1,2) = 7/2
===========================
Cheers,
Stan H.
===================