Two fixed points a (- C, 0), B (C, 0). The sum of the distances from the moving point P to the two fixed points is a constant 2A. Find the trajectory equation of point P

Two fixed points a (- C, 0), B (C, 0). The sum of the distances from the moving point P to the two fixed points is a constant 2A. Find the trajectory equation of point P

If a > C, then the trajectory is an ellipse, which is the definition of ellipse
So the trajectory of P is
x^2/a^2+y^2/b^2=1
b^2=a^2-c^2
The focus of a and B
A is the major axis, B is the minor axis
If C ≥ a, there is no solution

It is known that the square of the distance from the moving point P (x, y) to the origin is equal to the distance from it to the straight line L: x = m (M is a constant)

X ^ 2 + y ^ 2 = I M-X I, after removing the absolute value, we get two equations, x ^ 2 + y ^ 2 + x-m = 0 or x ^ 2 + y ^ 2-x + M = 0