The first line: let 3x+2y=k, then y=-3x/2+k/2, then this line is parallel or coincident with the straight line y=-3x/2, that is, regardless of the value of k, the straight line y=-3x+k/2 is parallel or coincident with y=-3x/2.

Because x and y satisfy (x-2)? +y？ =3, so the range of values of x and y is given in disguise.

As shown in the figure:

When the straight line y=-3x/2+k/2 takes point B, that is, when the straight line is translated to point B, the value of k is the maximum.

The specific method is as follows:

The second question can be proved in the same way.

The specific method is as shown in the figure:

I hope it helps you!