Find the asymptote of -4x^2 +y^2 -2y with a postive slope. Answer should be in equation of the form .

-4x^2 +y^2 -2y = 3      rewrite as

y^2 - 2y - 4x^2 = 3        complete the square on y

y^2 - 2y + 1 - 4x^2 = 3 + 1

(y - 1)^2  -   4x^2 =   4         divide both sides by 4

(y - 1)^2     -   x^2  

______         ____  =      1

   4                  1

In this form,   a = 2  , b = 1     h = 0    k = 1

The equation of the asymptote with the positive slope is 

y =  (a/b) ( x - h) + k        ....so...

y = (2/1) ( x - 0) + 1

y = 2x + 1

Here's the graph :   https://www.desmos.com/calculator/tenipf6zfq