According to what is known, the intersection of a straight line and two axes can be found, so the number of intersections between a circle with a diameter of AB and the straight line is the number of points C. Solution: According to the meaning of the question, the intersection of the straight line y=- 12x+2 with the X axis is (4,0), and the intersection with the Y axis is (0,2), as shown in the figure:

The intersection a is the intersection w (-4,4) between a vertical line and a straight line,

The intersection point b is the intersection point s (2, 1) of a vertical line and a straight line.

Passing through the midpoint E (- 1, 0) of AB, the intersection of vertical line and straight line is F (- 1, 2.5).

Then ef = 2.5 < 3,

Therefore, a circle with a radius of 3 and a center of E must have two intersections with a straight line.

There are four points that can form a right triangle with points A and B. 。

Therefore, D. Comments: This question is solved by using the properties of right-angled triangles and the positions of straight lines and circles.