Let the focus of parabola C: y = x ^ 2 be f, the moving point P move on the straight line L: x-y-2 = 0, and make two tangent lines PA and Pb of parabola C through P, which are tangent to parabola A and B respectively (1) Finding the trajectory equation of the center of gravity g of triangle APB (2) Prove ∠ PFA = ∠ PFB

Let the focus of parabola C: y = x ^ 2 be f, the moving point P move on the straight line L: x-y-2 = 0, and make two tangent lines PA and Pb of parabola C through P, which are tangent to parabola A and B respectively (1) Finding the trajectory equation of the center of gravity g of triangle APB (2) Prove ∠ PFA = ∠ PFB

Y = x ^ 2 = = > P = 1 / 2 let a (x1, X1 ^ 2), B (X2, X2 ^ 2) according to the tangent formula of parabola, the equation of AP is: 2x1x-y-x1 ^ 2 = 0 -------- (1) the equation of BP is: 2x2x2x2x-y-x2 = 0 -------- (2) (1), (2) the equation is: XP =

|Ab | = 2, the distance from the moving point m to the point a is 4, and the perpendicular Ma of MB intersects the point P. find the trajectory equation of the point P

Let a be the origin and B be on the positive x-axis, then the trajectory equation of P is:
Root sign (x ^ 2 + y ^ 2) = x + 3
It is difficult to write many mathematical symbols in the process of derivation

Point m divides segment AB into two parts: 3:4. If AB = 14cm, the distance between the midpoint of segment am and MB is 0______ ．

∵ am: MB = 3:4, ab = 14cm, ∵ am = 6cm, MB = 8cm, ∵ E and F are the midpoint of AM and BM respectively, ∵ EM = 3cm, MF = 4cm, ∵ the distance between AM and MB is EF = EM + MF = 7cm