The answer is b. There is a proof, but it is easily got by proving the other cases wrong.
Start off by combining like terms on the LHS (the terms with x in them).
So we get

Replacing this result with what we had before on the LHS, we get

⇒Solve for x (divide both sides

)
⇒Don't forget about reciprocity rules when dividing. This is the same as multiplying both sides by

⇒

⇒

***This is a proper fraction
Using the Pythagorean theorem we can solve for the radius
see attached picture:
To determine if it is a function or not, you can not have a vertical line drawn down the graph touch 2 of the graphed points. That means that you can not have 2 points with the same x value and different Y value. The first set of points satisfies this and is your answer. Hope that helps.