From

 (y-1)² = -8(x-2)

the -2 tells that the x-coordinate of the vertex is +2.
the -1 tells that the y-coordinate of the vertex is +1.
So the vertex is (1,2)

The fact that the sign before the 8 is negative tells us that the parabola
opens leftward. 

The fact that the x is in the expression that is not squared tells
us the that its axis of symmetry is horizontal, and opens right or left.

The absolute value of the -8, or 8, tells us two things.
1. 8 divided by 4, which is 2, is the distance between the vertex and the
focus (2 is also the perpendicular distance from the vertex to the
directrix). 

So the focus is 2 units from the vertex, inside the parabola.
So the focus is (0,1)

And the dirctrix is a vertical line 2 units from the vertex outside the
parabola, so it is the vertical line whose equation is y = 4.

2. The latus rectum (vertical distance across the parabola at the focus) is 8 units long.

The ends of the latus rectum is 4 units up and down from the focus, which
are (0,5) and (0,-3)



Edwin