For any real number k, what is the position relationship between the line (3K + 2) x-ky-2 = 0 and the circle x ^ 2 + y ^ 2-2x-2y-2 = 0? The relationship between the center of a circle and a straight line is discussed without over fixed point method

For any real number k, what is the position relationship between the line (3K + 2) x-ky-2 = 0 and the circle x ^ 2 + y ^ 2-2x-2y-2 = 0? The relationship between the center of a circle and a straight line is discussed without over fixed point method

3kx+2x-ky-2=0
(3x-y)=2-2x
When 3x-y = 0,2-2x = 0, the constant holds
x=1,y=3
So the straight line passes through the fixed point (1,3)
(x-1)²+(y-1)²=4
The distance between the centers (1,1) and (1,3) is 2, which is exactly equal to the radius
So the point is on the circle
So it's intersecting or tangent