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Section 12.12 : Cylindrical Coordinates
4. Convert the following equation written in Cylindrical coordinates into an equation in Cartesian coordinates.
\[z\,r = 2 - {r^2}\] Show SolutionThere is not really a lot to do here other than plug in \(r = \sqrt {{x^2} + {y^2}} \) into the equation. Doing this is,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{z\,\sqrt {{x^2} + {y^2}} = 2 - \left( {{x^2} + {y^2}} \right)}}\]