F is the focal point of the parabola y2 = 2x, m (3.2), P moves on the parabola, when PM + PF is the minimum, the coordinates of point P This is the content of elective 2-1 in senior two

The Quasilinear of parabola y ^ 2 = 2x is l: x = - 1 / 2
If PN ⊥ L is greater than N, then | PN | = | PF|
So, | PM | + | PF | = | PM | + | PN | ≥ | Mn|
Therefore, when p, m and N are the same line, the sum is the smallest
So, the ordinate of point P = 2
Abscissa of point P = 2 ^ 2 / 2 = 2
So, the coordinates of point P are: (2,2)

Point m (3,2), f is a parabola, y square = 2x, the focal point P moves on the parabola, and the minimum and maximum values of PM PF are obtained

From the question: MF & sup2; = (3-1 / 2) & sup2; + 2 & sup2; = 41 / 4
1. When the extension of MF intersects the parabola at P, then pm-pf "MF = root 41 / 2, so the maximum value of pm-pf = root 41 / 2
2. When the extension of FM intersects the parabola at P, then pm-pf-mf = - root 41 / 2, so the minimum value of pm-pf = - root 41 / 2

If the parabola y square = 12x, the moving point P, the focus F, the fixed point m (5,3), then the minimum value of PM + PF is

∵ point P is on the parabola y ^ 2 = 12x, let the coordinates of p be (a ^ 2 / 12, a). From y ^ 2 = 12x, the focal coordinates of the parabola are (3,0), and the Quasilinear equation of the parabola is x = - 3. Let PA ⊥ line x = - 3 cross point a through P, and obviously the coordinates of a are (- 3, a)

F is the focal point of the parabola y2 = 2x, m (3.2), P moves on the parabola, when PM + PF is the minimum, the coordinates of point P This is the content of elective 2-1 in senior two