can we create a unique circle with two

co-linear points

No,

consider the line joining your two points to be a chord of the circle
That chord could be the diameter of the circle or it could be near the edge of the circumference for a very large circle, thus there would be an infinite number of circles possible between these two positions.
So the circle is not "unique"

btw, any two points given would be co-linear, unless the two points coincide with each other.

No, it is not possible to create a unique circle with only two co-linear points. A circle is defined by its center and radius, and in order to uniquely determine a circle, you need a minimum of three non-co-linear points.

To understand why, consider that a circle is a set of points equidistant from its center. If you have two co-linear points, they only determine a line, not a circle. The two points could lie anywhere on that line, and there could be an infinite number of circles passing through those two points.

To uniquely define a circle, you need a third point that is not on the line defined by the first two points. The circle can then be constructed by finding the center as the intersection of the perpendicular bisectors of the three sides formed by the three points, and the radius as the distance between the center and any of the three points.

So, if you only have two co-linear points, you cannot create a unique circle.