mathscircles
posted by anoynomous on .
can we create a unique circle with two
colinear 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 colinear, unless the two points coincide with each other.