Find dy/dx if x^2+y^2=2xy

Question

A. x/(x-y)
B. (y+x)/(y-x)
C. 1
D. -x/y
E. None of these

Answer 1

Use implicit differentiation

x^2 + y^2 = 2xy

2x + 2y dy/dx = 2x dy/dx + 2y
2y dy/dx - 2x dy/dx = 2y - 2x
dy/dx(2y - 2x) = 2y-2x
dy/dx = (2y - 2x)/(2y - 2x) = 1
well, that was weird

let's see why ....

x^2+y^2=2xy
x^2 - 2xy + y^2 = 0
(x - y)^2 = 0
x - y = 0
y = x
ahhhh!, that explains it, we had simply a straight line in disguise.