If the distance between point m and point F (4,0) is less than 1, then the trajectory equation of point m is______ ．

According to the meaning of the question, the distance between point m and point F (4,0) is 1 less than the distance from point m to line L: x + 5 = 0, which means that the distance between point m and point F (4,0) is equal to the distance from point m to line L: x + 4 = 0, which satisfies the definition of parabola, so p = 8, the trajectory equation of point m is y2 = 16x, so the answer is: y2 = 16x

If the distance between the point m and f (0, - 2) is less than 1, then the trajectory equation of M is

If the distance between M and f (0, - 2) is 1 less than the distance from m to Y-3 = 0, then the distance between M and f (0, - 2) is equal to the distance from m to Y-2 = 0
Therefore, the trajectory of point m is a parabola with (0, - 2) as the focus and y = 2 as the Quasilinear. The equation is: x ^ 2 = - 8y

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