(4) Consider the set of points in R 3 that satisfy the equation (x − 0)2 + (y − 0)2 + (z − 1)2 = 1 in Cartesian coordinates. Either illustrate this set or give a geometric description of this set. Then convert this equation to spherical coordinates. Your equation should only include the variables ρ, ϕ, and θ.
Added by Eric S.
Step 1
The center of the sphere is at the point \((0, 0, 1)\) and the radius of the sphere is \(1\). Therefore, the set of points satisfying this equation is a sphere centered at \((0, 0, 1)\) with a radius of \(1\). Show more…
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