Question

I know that x^2 + y^2 in cartesian coordinates is r^2 in polar coordinates.

However, in my problem, I’m given x^2 + z^2. On a graph, it still forms a circle, except on a different plane than just x^2 + y^2.

Is it okay if I simplify x^2 + z^2 in my work to just r^2, or is that wrong?

Answer 1

Yes, it is okay to simplify x^2 + z^2 to r^2 in your work. This is because in polar coordinates, r represents the distance from the origin to a point, regardless of which plane the point is on.

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