Why a line is said to have infinite number of points? Is this so because a line is ever lasting or we can not count how many points does it have?
Finite means: Having an end.
Infinite means: No end!
So, if the answer is the first reason viz., line is ever lasting then a closed figure like circle, ellipse etc and even a line segment must be said to has finite number of points that is, we can't count it but they have a limit or simply we can say it's indeterminate! Is that so?
A line is said to have an infinite number of points because there are more than any finite number of points on the line. Between any two distinct points we can find a third point between those two, so we can locate any finite number of distinct points we wish on the line. It follows that there are more than any finite number of such points, i.e. there are infinitely many points on the line.
The same is true for a circle. Any finite number of distinct points can be found on a circle.
The same is true for a line segment with distinct endpoints. It contains infinitely many points.