Concept: The question tests on the fundamentals of Coordinate Geometry

Solution:

The number of points depends on the length of the radius. Now -7.5 is 2.5 points away from -5, which is the x co ordinate of the center.

So if the radius is 2, then x = -7.5 will cut 0 points on the circle.

If the radius = 2.5, then x = -7.5 will be a tangent at 1 point on the circle

if the radius is > 2.5, then x = -7.5 will cut 2 points on the circle.

Given that the circumference = 6π = 2πr. Therefore r = 3 which is greater than 2.5

There are 2 possible values of y.

Option C