Answer:
The correct option is C.
Step-by-step explanation:
The given equation is
[tex]-\frac{1}{4}(y+2)^2=(x-1)[/tex]
Multiply both the sides by -4.
[tex](y+2)^2=-4(x-1)[/tex] .... (1)
Where, (h,k) is vertex and (h+p,k) is focus.
The standard form of a parabola is
[tex](y-k)^2=4p(x-h)[/tex] ..... (2)
From (1) and (2), we get
[tex]k=-2,h=1,4p=-4\Rightarrow p=-1[/tex]
The focus of the parabola is
[tex](h+p,k)=(1-1,-2)=(0,-2)[/tex]
The focus of the given parabola is (0,-2). Therefore the correct option is C.
