Find the tangent equation parallel to the straight line y = 2x on the curve y = x & #

Find the tangent equation parallel to the straight line y = 2x on the curve y = x & #

A:
y=x²
Derivation: y '(x) = 2x
If the tangent is parallel to y = 2x, then the slope k = 2
Let k = y '(x) = 2x = 2
The solution is: x = 1
Substituting y = x & # 178, we get y = 1
So: tangent point (1,1), tangent slope k = 2
So: the tangent is Y-1 = 2 (x-1)
The solution is y = 2x-1

How to solve the equation xy = 2x + 2Y?
Smart people to answer!

This is a binary equation. If only xy = 2x + 2Y, there will be infinite sets of answers, such as x = 0, y = 0; X = 1, y = - 2, etc