Equation of a cylinder in the XYZ Space

Question

Write the equation for the graph in the $xyz$-space of all the points that lie on the cylindrical tube $4$ units away from a center line defined by $\{(x, y, z)| y = -2, z = 3\}$.

Would it be $$(y+2)^2 + (z-3)^2 = 16$$

Answer 1

Your equation is correct. In a 2D world, that equation would represent a circle like this:

In a 3D world it represents a cylinder. This is basically the $(x - x_0)^2 + (y - y_0)^2 = r^2$ equation moved to the $yz$ plane.