10. (Bonus) Express the surface $x^2 - y^2 + z^2 = 4$ in spherical coordinates. Simplify (use appropriate trig identities) and write the equation in terms of $\rho$.
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Step 1: The conversion from Cartesian coordinates (x, y, z) to spherical coordinates (\rho, \theta, \phi) is given by: x = \rho sin(\phi) cos(\theta) y = \rho sin(\phi) sin(\theta) z = \rho cos(\phi) Show more…
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