Final answer:
To find the radius of a circle from two points on the circumference, you need either the coordinates of the center or the equation of the circle. The slope of the line connecting the points is irrelevant, while the distance between the points alone is insufficient without knowing where the center is.
Step-by-step explanation:
Finding the radius of a circle from two points requires the distance between the points and the coordinates of the center of the circle. If you only have two points on the circumference of a circle, you cannot determine the radius without additional information. The distance between two points gives you the length of a chord of the circle, but without knowing where the center is, the radius remains undetermined. However, if you have the coordinates of the center of the circle, you can use the distance formula to calculate the radius by measuring the distance from the center to either of the two points on the circle.
If you have the equation of the circle, it often contains the radius explicitly, or it can be calculated from the parameters of the equation if it's in the standard form (x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius.
The slope of the line connecting the two points is irrelevant in finding the radius of the circle, as it does not provide information about the circle's size or position, unless combined with other specific information that links the points to the circle's diameter.