Analysis: 1, converted into cyclic standard equation (X- 1) 2+(Y-2) 1 = 5,

The center of the circle (1, 2) and the radius R=√5,

Then the distance from the center of the circle to the straight line d = │1+4-5+√ 5 │/√ (1+4) =1,

∴(AB/2)^2+d^2=R^2，

(AB/2) 2+ 1 = 5，AB=4。

2, the straight line is (3x-y+3)a+(x+y+ 1)=0,

When 3x-y+3=0 and x+y+ 1)=0, x=- 1, y=0,

That is, the straight line passes through the (-1, 0) point.

(- 1) 2+0+4 * (- 1) =-3 < 0,

The point (-1, 0) is in the garden.

So straight lines and circles intersect.