The focus is a point and the directrix is a line.
The parabola has the equation as follows:
(x - h)² = 4p(y - k)
where (h,k) is the vertex, p is the distance from
the vertex to the focus and also the distance from the vertex to the focus. The focus is (h, k + p) and the directrix is y = k - p
We can now write the equation.
(x - h)² = 4p(y - k)
(x - 1)² = 4p(y - 2)
y= 2.5 = k-p = 2 - p
p = -0.5
(x - 1)² = 4(-0.5)(y - 2)
(x - 1)² = -2 (y - 2)
The focus would be
(1 , 2 + -0.5)
(1 , 1.5 )
