Vertex = (0, 4) & Focus = (0, 2)
The distance between the vertex and directrix is same as the distance between the vertex and focus.
Directrix is y – 6 = 0
For any point of P(x, y) on the parabola
Distance of P from directrix = Distance of P from focus
Perpendicular Distance (Between a point and line) = 
whereas the point is (x1, y1) and the line is expressed as ax + by + c = 0 i.e.., x(0) + y – 6 = 0 & point = (x,y)
Distance between the point of intersection & centre
[Distance Formula] {Between (x,y) & (0,2)}
Squaring both the sides,
x2 + y2 - 4y + 4 = (y – 6)2
x2 + y2 - 4y + 4 = y2 - 12y + 36
x2 + 8y – 32 = 0
Hence, the required equation is x2 + 8y – 32 = 0.
