In order to solve the problem, we can first set the point in the first quadrant of the plane rectangular coordinate system, and the coordinate is (3,4).

1, when it intersects with the coordinate axis r = 3, the circle is tangent to the y axis.

2. There are two intersections with coordinate axis 3 < r < 4. At this time, the circle intersects with the X axis and the Y axis.

3. There are three intersections with the coordinate axis r = 4 or 5.

4. There are four intersections with the coordinate axis 4 < r < 5 or r > 5.

In other cases, and so on ——