I need help finding a tangent line

Question

So I'm supposed to find the tangent line of the anti derivative of y=(y^2)/(x-1) when x = 2.

I think I keep messing stuff up so if someone could explain that would be great.

Answer 1

If x = 2, yhen y = y² or y(y - 1) = 0; y = 0 or y = 1

We have 2 tangent points:(2, 0) and (2, 1).

Now we have yx - y = y²;

Implicit differentiation give us: y'x + y - y' = 2yy'; y'(x - 2y - 1) = - y; y' = y/(2y + 1 - x)

For point (2,0) y' = 0 and tangent line is y = 0

For Point (2,1) y' = 1 and tangent line is y = 1 + 1(x - 2); y = x - 1