Find the asymptote of -4x^2 + y^2 - 2y = 3with positive slope.

This will be a vertical hyperbola with the following equation

(y - 1)^2     -    x^2

______           ___      =     1

    4                   1

In the following form

(y - k)^2    -   (x - h)^2

______         ______      =  1

   a^2                b^2

The center is  ( h, k)   =   (0, 1)

The slope of asymptote with the positive slope, m, is    a / b   =  2 / 1  = 2

And the equation of this line is

y =  m ( x - h) + k  =     2 (x - 0) + 1     =     2x + 1