Given circle C1: (x + 3) ^ 2 + y ^ 2 = 1 and circle C2: (x-3) ^ 2 + y ^ 2 = 9, the moving circle m is circumscribed with circle C1 and C2 at the same time The orbit equation of moving circle center M

Given circle C1: (x + 3) ^ 2 + y ^ 2 = 1 and circle C2: (x-3) ^ 2 + y ^ 2 = 9, the moving circle m is circumscribed with circle C1 and C2 at the same time The orbit equation of moving circle center M

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Given circle C1: (x + 3) 2 + y2 = 1 and circle C2: (x-3) 2 + y2 = 9, the moving circle m is circumscribed with circle C1 and circle C2 at the same time

The center of moving circle m (x, y) is set M (x, y), and the tangent points of moving circle m and C1, C2 are respectively a and B, then | MC1 | - ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||c2 | = 6, which is defined by hyperbola: the locus of the moving point m is determined by

It is known that parabola C1: y ^ 2 = 4x circle C2: (x-1) ^ 2 + y ^ 2 = 1, the line L passing through the focus of parabola intersects C1 at two points a and D, and intersects C2 at two points B.C
1. The value of | ab | * | CD |
2. Whether there is a straight line L, such that K (OA) + K (OB) + K (OC) + K (OD) = 3 √ 2, and | ab |, | BC |, | CD | are in the sequence of equal difference numbers. If there is, find all the straight lines L that meet the conditions. If not, explain the reason

1. The directrix of C1 is y = - 1, and the focal point is (1,0). It can be seen from the drawing that the lengths of AB and CD are abscissa values of a and D respectively. Let the linear equation over the focal point be y = K (x-1), and the abscissa values of a and D solved by C1 are [square root of K ^ 2 + 2-2 * (k ^ 2 + 1)] / K ^ 2 and [square root of K ^ 2 + 2 * (k ^ 2 + 1)] / K ^ 2 respectively. Multiply the two values and the result is 1. That is, the product is independent of K
2. AB, BC, CD length range arithmetic sequence, then AB + CD = 2 * BC = 4, have the above question can get k = 2 or K = - 2, from the first question can find out the coordinates of all points, the corresponding slope is y coordinate divided by X coordinate, the result obtained, substituted into two possible K values, does not meet the slope sum condition