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Write the equation of the tangent at (2,2) to the curve x^2-2xy+y^2+2x+y-6=0

Can anyone please give me some ideas to do it?Thanks!

3 answers

first you have to differentiate implicitly with respect to x

2x - 2xdy/dx - 2y + 2ydy/dx + 2 + dy/dx = 0
now solve this for dy/dx by using common factors
dy/dx(2y - 2x + 1) = -2x + 2y + 2
dy/dx = (-2x+2y+2)/(2y-2x+1)

now sub in x = 2 from your point (2,2) to get the slope of the tangent.

from there it should be easy, let me know what you got.
Is it y=2x-2?
correct
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