If the vertex of the parabola is O, the focus is f, and M is the moving point on the parabola, then the value range of | Mo | / | MF |

If the vertex of the parabola is O, the focus is f, and M is the moving point on the parabola, then the value range of | Mo | / | MF |

Let m (x, y). From the point m on the parabola, y ^ 2 = 2px (P > 0). (1)
K = | Mo | / | MF |, then from the definition of parabola, we can know: | Mo | = x + P / 2,
There is | Mo | ^ 2 = (k * | MF |) ^ 2, that is: x ^ 2 + y ^ 2 = [K (x + P / 2)] ^ 2. (2)
From (1), (2), we get x ^ 2 + 2px = k ^ 2 [x ^ 2 + PX + (P ^ 2) / 4]
That is, (k ^ 2-1) x ^ 2 + (k ^ 2-2) PX + (k ^ 2) (P ^ 2) / 4 = 0, k > = 0, any real number can be taken for X
There are (PK ^ 2-2p) ^ 2-4 (k ^ 2-1) (k ^ 2) (P ^ 2) / 4 > = 0. P > 0
4-3k ^ 2 > = 0
0 required=