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Cylindrical and spherical coordinates.

Write the equations

i) x^2 - y^2 - 2z^2 = 4 and

ii) z = x^2 - y^2 in

a) cylindrical coordinates
b) spherical coordinates

give detailed explanation for each step of the solutions.

Solution Preview

i.)
a.)
phi == p = angle in x-y plane with respect to X-Z plane
x = r*cos(p)
y = r*sin(p)
z = z
substitute the values in x^2 - y^2 - 2z^2 = 4
=> r^2 * cos^2(p) - r^2 * sin^2(p) - 2z^2 = 4
=> r^2 * cos(2*p) - 2z^2 = 4 ...

Solution Summary

Cylindrical and spherical coordinates are determined.

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