Given that circle C1: x ^ 2 + y ^ 2-2mx + 4Y + m ^ 2-5 = 0, circle C2: x ^ 2 + y ^ 2 + 2x-2my + m ^ 2-3 = 0, what is the value of M Given the circle C1: x ^ 2 + y ^ 2-2mx + 4Y + m ^ 2-5 = 0, circle C2: x ^ 2 + y ^ 2 + 2x-2my + m ^ 2-3 = 0, what is the value of M (1): circle C1 and circle C2 are circumscribed, and the equation of the inner common tangent is obtained. (2) circle C1 and circle C2 are included

Given that circle C1: x ^ 2 + y ^ 2-2mx + 4Y + m ^ 2-5 = 0, circle C2: x ^ 2 + y ^ 2 + 2x-2my + m ^ 2-3 = 0, what is the value of M Given the circle C1: x ^ 2 + y ^ 2-2mx + 4Y + m ^ 2-5 = 0, circle C2: x ^ 2 + y ^ 2 + 2x-2my + m ^ 2-3 = 0, what is the value of M (1): circle C1 and circle C2 are circumscribed, and the equation of the inner common tangent is obtained. (2) circle C1 and circle C2 are included

(1) Circle 1 Center (m, - 2) R1 = 3, circle 2 Center (- 1, m) R2 = 2
（m+1)^2+(m+2)^2=25,
M = 2 or - 5;
Now {x ^ 2 + y ^ 2-4x + 4y-1 = 0, x ^ 2 + y ^ 2 + 2x-4y + 1 = 0}
Or {x ^ 2 + y ^ 2 + 10x + 4Y + 20 = 0, x ^ 2 + y ^ 2 + 2x + 10Y + 22 = 0}
We get 3x-4y + 1 = 0
Or 4x-3y-1 = 0
(2)（m+1)^2+(m+2)^2=1,
M = - 2 or - 1