Answer:
The equation of the parabola is \((x-2)^2=-4(y+1)\).
Step-by-step explanation:
The standard form of the parabola is,
\((x-h)^2=4p(y-k)\)
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
\((h,k+p)=(2,-2)\)
\(h=2\)
\(k+p= -2\) ... (1)
Since directrix is y=0,
\(k-p=0\) ... (2)
Add equation 1 and 2.
\(2k=-2\)
\(k=-1\)
Put this value in equation 2.
\(-1-p=0\)
\(p=-1\)
Now we have p= -1, k= -1and h=2.
The equation of the parabola is,
\((x-2)^2=4(-1)(y+1)\)
\((x-2)^2=-4(y+1)\)
Therefore the equation of the parabola is \((x-2)^2=-4(y+1)\).
