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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.
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