when the vertex of the parabola equation is: (h, k) and the focus is: (x1, y1), then the vertex equation of the parabola is:

(X-h)² = 4a(Y-k)；  ( a = √(h-x1) * (h-x1) + (k - y1) * (k-y1) )

standard form of parabola equation:

Y = (1/4a)X² - (h/2a)X + (k + h²/4a)；( a = √(h-x1) * (h-x1) + (k - y1) * (k-y1) )