Given the circle (x+2)2+y2=36, the radius of the center m (-2,0) is 6.

A is any point on the circle, AM=6.

N (2 2,0), the distance from any point on the middle vertical line of line segment AN to both ends is equal, and the intersection point MA is at point P. 。

There is PN=PA

And am = pa+pm = 6；; That is, PM+PN=6.

That is to say, the sum of the distances from the moving point P to the two fixed points M and N is a constant of 6; According to the definition of ellipse, the parameters in ellipse

2a=6，a=3，

The focal length 2c=4, c=2,

So b=√(3? -2? )=√5

Elliptic equation: x? /9+y？ /5= 1