10.1#5

So, I got the first question right. I understand what I need to do for the second one. It's the equation of the circle that you get when the sphere passes through that z-plane. However, I don't know how to figure out the radius.

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Yeah, you did solve the first part.  The general principle for the second is to recognize the information that they're giving you to solve the problem, in this case that's knowing in the intersection of the sphere with the plane z=3 means that in the intersection z=3, z is equal to 3, so just replace z by 3 and simplify and that will give you what you need instead of 1/3.