Tangents are drawn to the curves x^2*y=1-y at the points where it is met by the curve x*y=1-y . The point of intersection of these tangents is :-

Hmm...that's a though one...

Maybe if you form a system of equations like this:

x^2*y=1-y
x*y=1-y

I already solved it. The answer is: x = 1 and y = 1/2

Could that be the point (1, 1/2) you are looking for?

Regards!