It is known that the difference between the distance from a moving point P to point F (1.0) in the plane and the distance from point P to y axis is equal to 1 The equation for finding the locus C of the moving point P

It is known that the difference between the distance from a moving point P to point F (1.0) in the plane and the distance from point P to y axis is equal to 1 The equation for finding the locus C of the moving point P

√（（x-1）²+y²）-|x|=1
That is, (x-1) ² + Y & #178; = (1 + |x|) ²
When x ≥ 0, | x | = x, (x-1) &# 178; + Y & # 178; = (1 + x) &# 178;
y²=4x
When x ≤ 0, | x | = - x (x-1) &# 178; + y &# 178; = (1-x) &# 178;
y²=0,y=0
If the image passes through the origin, the left side of the origin is a line coincident with X, and the right side is a parabola with X axis as the symmetry axis, origin as the vertex, and f (1,0) as the focus