It is known that the sum of the distances between the moving point P and the two focuses F1 and F2 of hyperbola 2x ^ 2-2y ^ 2 = 1 is 4 (1) The equation of trajectory C of moving point P is obtained; (2) If M is the moving point on the curve C, take M as the center and MF2 as the radius to make the circle M. if there are two intersections between the circle m and the Y axis, calculate the value range of abscissa of the point M

It is known that the sum of the distances between the moving point P and the two focuses F1 and F2 of hyperbola 2x ^ 2-2y ^ 2 = 1 is 4 (1) The equation of trajectory C of moving point P is obtained; (2) If M is the moving point on the curve C, take M as the center and MF2 as the radius to make the circle M. if there are two intersections between the circle m and the Y axis, calculate the value range of abscissa of the point M

1) Let p be p (x, y) because in the hyperbola 2x & # 178; - 2Y & # 178; = 1, a & # 178; = B & # 178; = 1 / 2, so C & # 178; = A & # 178; + B & # 178; = 1, the focus coordinates of the hyperbola are F1 (- 1,0), F2 (1,0) according to the meaning of the title, √ (x + 1) &# 178; + Y & # 178; + √ (x-1) &# 178; + Y & # 178; = 4x & #