Given the curve of C defined by the equation x^2 - 2xy +y^4 =4.

Question

1) Find the derivative dy/dx of the curve C by implicit differentiation at the point P= (1,-1).

2) Find a line through the origin that meets the curve perpendicularly.

Answer 1

take d/dx

2x -2y -2xy' + 4y^3y' = 0

plug in 1 for x and -1 for y

2 + 2 - 2y' - 4y' = 0

4 = 6y'

y' = 2/3