1) If the center of the circle is set to O(3, a) on the vertical line of AB, then:

R 2 = (3- 1) 2+(a-0) 2 = 5, a = 1 or a=- 1.

So the center of the circle is (3, 1) or (3, 1).

So the standard equation of a circle is (x-3) 2+(y+ 1) 2 = 5 or (x-3) 2+(y- 1) 2 = 5.

2) Let the center of the circle be O 1(0, b), then o1a = o1b.

Namely, (-1-0) 2+(4-b) 2 = (3-0) 2+(2-b) 2.

B= 1。

So the center of the circle is (0, 1)

r^2=(- 1-0)^2+(4- 1)^2= 10

So the standard equation of a circle is: x 2+(y-1) 2 =10.