The midpoint algorithm shall be applied to drawing a part of the graph of the function y = −a √x + b (a,b ∈ N+). (a) For which x-values is the slope between −1 and 0? (b) Rewrite the function in a...

The midpoint algorithm shall be applied to drawing a part of the graph

of the function y = −a

√x + b (a,b ∈ N+).

(a) For which x-values is the slope between −1 and 0?

(b) Rewrite the function in a suitable implicit form F (x, y) = 0. Use d = F (x, y)

as a decision variable to develop the midpoint algorithm. How does d change

depending on whether the eastern (E) or the south-eastern (SE) point was drawn

in the previous step of the midpoint algorithm?

(c) How should the initial value dinit for d be chosen, if (x0, y0) = (a2,−a2 + b) is

the first point of the curve to be drawn?

(d) How can the rational values for the decision variable be avoided?