1. Let the center of the circle be on the straight line 3X+Y-5=0, and the center of the circle be (a, 5-3a).

The equation of a circle is (x-a)? +(y+3a-5)？ =r？

A circle passes through the sum of the origin (3,-1).

Answer? +(3a-5)？ =r？ =(3-a)？ +(- 1+3a-5)？

A=5/3, then r=5/3.

The equation for finding a circle is (x-5/3)? +y？ =25/9

2. Find the center of a straight line 3X+2Y=0, and let the center be (a, -3/2 a).

The equation of a circle is (x-a)? +(y+3/2 a)？ =r？

The intersection points of the circle and the X axis are (-2,0) and (6,0) respectively.

(-2-a)？ +(0+3/2 a)？ =r？ =(6-a)？ +(0+3/2 a)？

If a=2, then r=5.

The equation for finding a circle is (x-2)? +(y+3)？ =25