The equation of parabola C1 is (Y-2) ^ 2 = - 8 (x + 2). Curve C2 and C1 are symmetric about point (- 1,1). Find the equation of curve C2

The equation of parabola C1 is (Y-2) ^ 2 = - 8 (x + 2). Curve C2 and C1 are symmetric about point (- 1,1). Find the equation of curve C2

On point (- 1,1) symmetry
(x1+x2)/2=-1
x2=-2-x1
(y1+y2)/2=1
y2=2-y1
So replace x with - 2-x
Y is replaced by 2-y
So (2-y-2) = - 8 (- 2-x + 2)
y²=8x

It is known that the equation of curve C is y = x ^ 2-2x + 2 to find the equation of curve C which is symmetric with respect to line x-y-3 = 0
As explained on the first floor, which expert answers my question, I will score + + + points

From x-y-3 = 0, y = x-3, x = y + 3 are substituted into the curve equation
Simplify
x=y^2+4y+8