It is known that the distance between line L and points a (3,3) and B (5,2) is equal, and it passes through the intersection of two lines l1:3x-y-1 = 0 and L2: x + Y-3 = 0, then the equation of line L is

If the distance between L and ab is equal, then l must pass the midpoint of ab
Let the midpoint of AB be C, then C (4,2.5)
Then find the intersection D of L1 and L2
Get D (1,2)
Let l be y = ax + B
Two points of CD are brought in, a = 1 / 6, B = 11 / 6
So the equation of L is x-6y + 11 = 0

It is known that the distance between line L and points a (3,3) H and B (5,2) is equal, and it passes through the intersection of line l1:3x-y-1 = 0 and line L2: x + Y-3 = 0. The equation of line L is obtained

Intersection (1,2)
Let y = kx-k + 2
l2k-1l=l4kl
12k^2+4k-1=0
K = - 1 / 2 or 6
L1 y=-1/2x+5/2
L2 y=6x-4

Given that the distances between points a (3,3), B (5,2) and line L are equal, and line L passes through the intersection of two lines l1:3x-y-1 = 0 and L2: x + Y-3 = 0, the equation of line L is obtained

(1) if a and B are on the same side of the line L, then l ‖ AB, KAB = 3 − 23 − 5 = - 12, the equation of the line is Y-2 = - 12 (x-1), that is, x + 2y-5 = 0. (2) if a and B are on the opposite side of the line L, then the line L passes through the middle point (4, 52) of the line AB, and the two-point equation of the line L is y − 2x − 1 = 52 − 24 − 1, that is, x-6y + 11 = 0 In summary (1) (2), we know that the equation of line L is x + 2y-5 = 0 or x-6y + 11 = 0

It is known that the distance between line L and points a (3,3) and B (5,2) is equal, and it passes through the intersection of two lines l1:3x-y-1 = 0 and L2: x + Y-3 = 0, then the equation of line L is