How many common tangents are there between two circles C1: x ^ 2 + y ^ 2 = 1 and C2: (x + 3) ^ 2 + y ^ 2 = 4?

Three common tangent lines
x^2+y^2=1
The center of the circle is (0,0) and the radius is 1
（x+3）^2+y^2=4
The center of the circle is (- 3,0) and the radius is 2
The center distance is 3 = R1 + R2 = 1 + 2 = 3
Two circles circumscribed
There are three common tangents in circumscribed
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It is known that the equation of curve C1 is x ^ 2-y ^ 2 / 8 = 1 (x > = O, Y > = 0), the equation of circle C2 is (x-3) ^ 2 + y ^ 2 = 1, the line L with slope k (k > 0) is tangent to circle C2, the tangent point is a, the line L and curve C1 intersect at point B, | ab | = root 3, then the slope of AB is（
A. Root 3 B.1 / 2 C.1 D. root 3

The center of C2 is C (3,0), the radius is r = 1 x & # 178; - Y & # 178; / 8 = 1, X ≥ 0, y ≥ 0 is the part of hyperbola in the first quadrant. | AC | = r = 1| ab | = √ 3aC ⊥ AB, | BC | &# 178; = | AC | &# 178; + | ab | &# 178; = 1 + 3 = 4, that is, B is a circle (x - 3) &# 178; + Y & # 178; =

Given the curves C1: y = e ^ X and C2: y = - 1 / e ^ x, if the tangents of C1C2 at points P1 and P2 are the same line L, try the equation of L

C1: y '= e ^ x, C2: y' = e ^ (- x), if there is the same straight line, then e ^ (x1) = e ^ (- x2), and e ^ x is a monotone increasing function, so X1 = - X2, that is, X1 and X2 are symmetric about y axis. Because the straight line passes through x1, X2, that is, through the point (x1, e ^ (x1), (X2, - 1 / e ^ (x2) = (- x1, - e ^ (x1)), so the straight line passes through the origin, let it be y = KX. K = y '

The equation of curve C1: y = 2x ^ 2 with respect to the symmetric curve C2 of line x = - 2 is
Please explain how to solve this problem

c2:y=2(x+4)^2

How many common tangents are there between two circles C1: x ^ 2 + y ^ 2 = 1 and C2: (x + 3) ^ 2 + y ^ 2 = 4?