Answer:
y = - 3
Step-by-step explanation:
The general form of the equation of a parabola is given by:
[tex](y-k)^2=4p(x-h)[/tex]
with foci (h,k) and directrix equation given by y = k - p.
The parabola equation that you have is
[tex]y^2-4x+4y-4=0[/tex]
you complete squares to get the general form of the equation:
[tex](y^2+4y+4)-4-4=4x\\\\(y+2)^2=4x+8\\\\(y+2)^2=4(x-(-\frac{8}{4}))\\\\(y+2)^2=4(1)(x-(-2))[/tex]
[tex](y-(-2))^2=4(1)(x-(-2))[/tex]
Next, you compare the last expression with the general for of the equation of a parabola and you obtain:
[tex]k = -2\\\\h=-2\\\\p=1[/tex]
hence, the directrix equation is y = k - p = - 2 - 1 = - 3
