points equidistant from a point in 3D are the surface of a sphere.
So, your two constraints will be the intersection of two spheres, which is a circle.
Naturally, the intersection will lie in the x-y plane, since the centers of the spheres are both on the z-axis.
Your circle is indeed x^2+y^2 = 3. It just happens to lie in the plane z=0. Technically, x^2+y^2=3 is a cylinder centered on the z-axis.
Describe the given set with a single equation or with a pair of equations.
The set of points in space that lie 2 units from the point (0,0,1) and, at the same time, 2 units from the point (0,0,-1).
I wrote distance equations for both set them equal to each other and got z=0. Then, I plugged in 0 for z and got x^2+y^2=3. I'm just not sure what the answer would be. Is it z=0 or x^2+y^2=3?
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