Answer:
The equation of the parabola is [tex](x-2)^2=-4(y+1)[/tex].
Step-by-step explanation:
The standard form of the parabola is,
[tex](x-h)^2=4p(y-k)[/tex]
Where, (h,k+p) is focus and directrix is y=k-p
It is given that the focus of (2,-2) and a directrix of y = 0
[tex](h,k+p)=(2,-2)[/tex]
[tex]h=2[/tex]
[tex]k+p= -2[/tex] ... (1)
Since directrix is y=0,
[tex]k-p=0[/tex] ... (2)
Add equation 1 and 2.
[tex]2k=-2[/tex]
[tex]k=-1[/tex]
Put this value in equation 2.
[tex]-1-p=0[/tex]
[tex]p=-1[/tex]
Now we have p= -1, k= -1and h=2.
The equation of the parabola is,
[tex](x-2)^2=4(-1)(y+1)[/tex]
[tex](x-2)^2=-4(y+1)[/tex]
Therefore the equation of the parabola is [tex](x-2)^2=-4(y+1)[/tex].
