(m+ 1)(x-4)+2(y-0)=0

L constant intersection (4,0) No matter what m is.

So the equation of the circle is:

(x-4)^2+y^2= 16

The equation of circle m is (x-4-7cosa) 2+(y-7sina) 2 =1.

The locus of the center is: a circle with the center of C (4 4,0) and the radius of 7!

Consider the symmetry of a circle.

As long as we discuss: when cosA= 1, the equation of m is (x-11) 2+y 2 =1.

The vector CE point is multiplied by the vector CF = 4 2 * COS angle ECF= 16cos angle ECF.

Therefore, it can be transformed into a plane geometry problem to solve.

The radius of circle C is: 4, the radius of circle M is: 1, and the center distance is CM=7.

There is a moving point p on m, which makes two tangents with circle c, and the tangents are e and f.

Find the ECF of cosine angle.

Maximum value-1/9, minimum value-1/2.

therefore

Vector CE point multiplied by vector CF

Maximum value =- 16/9

Minimum value =-8