It is known that the center of ellipse C is at the coordinate origin and the focus is on the X axis. The maximum distance from the point on ellipse C to the focus is 3 and the minimum is 1. Then: a = (3+ 1)/2 = 2, c = 1, b = √ 3.

So the equation of ellipse C is: x 2/4+y 2/3 =1.

If the straight line L: Y = KX+B intersects with ellipse C and two points A and B (A and B are not left and right vertices), and the circle with diameter AB passes through the right vertex of ellipse C, the coordinates of point C are (2,0), and the coordinates of point AB are (x 1, y 1), (x2,

Simultaneous linear equation and elliptic equation: 3x 2+4 (kx+b) 2 = 12.

Simplification: (4k 2+3) x 2+8kbx+4b 2- 12 = 0 \

Then: x1+x2 =-8kb/(4k2+3); x 1x2=(4b^2- 12)/(4k^2+3)

y 1 = kx 1+b； y2=kx2+b

y 1/(x 1-2)=-(x2-2)/y2

(kx 1+b)(kx2+b)+(x 1-2)(x2-2)= 0

k^2x 1x2+kb(x 1+x2)+b^2+x 1x2-2(x 1+x2)+4=0

(k^2+ 1)(4b^2- 12)/(4k^2+3)-(kb-2)*8kb/(4k^2+3)+b^2+4=0

(k^2+ 1)(4b^2- 12)-(kb-2)8kb+(b^2+4)(4k^2+3)=0

4k^2b^2- 12k^2+4b^2- 12-8k^2b^2+ 16kb+4k^2b^2+3b^2+ 16k^2+ 12=0

4k^2+7b^2+ 16kb=0

k=2b 3b/2

When k=2b+3b/2=7b/2, the linear equation is: y=b(7x/2+ 1), crossing the fixed point (-2/7,0).

When k=2b-3b/2=b/2, the linear equation is: y=b(x/2+ 1), crossing the fixed point (-2,0).