According to the definition of isosceles triangle, AB=AC is obtained.
So (4-3) 2+(2-5) 2 = (4-x) 2+(2-y) 2.
So (x-4) 2+(y-2) 2 = 10.
The trajectory equation of C is: (x-4) 2+(y-2) 2 = 10.
It is a circle with the center (4,2) as the center and the root number 10 as the radius.
I hope I can help you, please adopt it.