The distance from the point on the curve m to the point F (1,0) is smaller than the distance from it to the straight line L: x + 2 = 0,

The distance from the point on the curve m to the point F (1,0) is smaller than the distance from it to the straight line L: x + 2 = 0,

The distance from point to point F (1,0) on curve m is 1 less than the distance from point to line L: x + 2 = 0, that is to say, the distance from point to point F (1,0) on curve m is equal to the distance from point to line L: x + 1 = 0. With the definition of parabola, the equation y & # 178; = 2px of curve m is obtained
P/2=1 P=2
∴y²=4x

It is known that the distance from the moving point P to the point F (1,0) in the plane is smaller than the distance to the straight line x = -- 2. The equation for finding the trajectory C of P

Set point P (x, y)
|X-(-2)|-√[(X-1)^2+Y^2]=1
|X+2|-1=√[(X-1)^2+Y^2]
When x + 2 ≥ 0
X+1=√[(X-1)^2+Y^2]
The square of both sides is x ^ 2 + 2x + 1 = x ^ 2-2x + 1 + y ^ 2
4X-Y^2=0
When x + 2