To find the equation of the circle circumscribing the given rectangle, we can follow these steps:

Step 1: Find the intersection points of the diagonals of the rectangle.
Step 2: Find the midpoints of the diagonals.
Step 3: Find the distance between the midpoints.
Step 4: Use the distance as the radius to find the equation of the circle.

Step 1: Find the intersection points of the diagonals
To find the intersection points of the diagonals, we can solve the equations of the diagonals simultaneously.

Given equations of the diagonals:
1) 2x - y + 3 = 0
2) 2x - y - 4 = 0
3) x + 2y - 1 = 0
4) x + 2y - 2 = 0

Solve equations 1) and 2) simultaneously:
2x - y + 3 = 2x - y - 4
7 = -4

This equation is inconsistent, which means the diagonals do not intersect. Therefore, the given rectangle is not a valid rectangle.

Explanation:
Since the diagonals of a rectangle must intersect, we can determine whether the given lines form a rectangle by checking if their intersection points exist. In this case, when we solve equations 1) and 2), we find an inconsistency (7 = -4), which means that the lines are parallel and do not intersect. Hence, the given lines do not form a rectangle.

Conclusion:
The given lines do not form a valid rectangle, and therefore, we cannot find the equation of the circle circumscribing it.