Find the formulas of the middle point algorithm for drawing the parabola?

Find the formulas of the middle point algorithm for drawing the parabola ?
x^2 = 4*(a+b)*y , a,b > 0.
Solve it according to E(East) and NorthEast(NE) ?

This is the result i got (This is writen in java frame, so its the opposite on graph)

This is my try, Ok in this problem the y increases y_{k+1} = y_k + 1 every time and x_{k+1} = x_k or x_k + 1 depending on the P_k value. Here is code i tried with: If P_{k} > then ( p_{k+1} = p_k – 4*(a + b) + 2x_k + 1; and x in increased by one x_{k+1} = x_k + 1;) else ( p_{k+1} = p_k – 4(a + b);) , It doesn’t look very well i think