Thank you for the opportunity to help you with your question!

Let ( x₀ , y₀ ) be any point on the parabola.

 Find the distance between (x₀ , y₀) and the focus. Then find the distance between (x₀ , y₀) and directrix. Equate these two distance equations and the simplified equation in x₀ and y₀ is equation of the parabola.

The distance between (x₀ , y₀) and (2, -1) is

sqrt((x-2)^2 + (y-(-1))^2)

(x₀ , y₀) and the directrix, y = -1/2 is

| y₀– -1/2|.

Equate the two distance expressions and square on both sides.

(x-2)^2 + (y-(-1))^2) = (y+1/2)^2

answer is D.