The question given here is from the January 2016 Algebra II/Trig Regents in New York State
I have one major issue with this question.
A student needs to know nothing about circles and their equations. The point (3,-5) makes only one of the four choices true. All a student had to know was which number was x, which was y, and then substitute them in and do the arithmetic.
Yes, the student had to know something. But they had to know nothing about circles.
Please take note that the pair (0,-2) does not satisfy any of the equations.
I can guess at the design behind the question: the student has to know the standard form of the equation of a circle, what to substitute in for its parameters, and how to "wrap up" to identify the radius and complete the solution. As an "fill-in-the-blank" questions this would be fine.
As multiple choice, with the choices it has, it stinks.