Question

Identify the surface and convert to cylindrical and spherical coordinates:

x^2 - y^2 + z^2 - 4x - 2y - 2z + 4 = 0

Answer 1

I've identified it as an elliptical cone with equation (y+1)^2 = (z-1)^2 + (x-2)^2, but am having trouble with conversions

Answer 2

good

Answer 3

Cylinder cordinate is
(r,theta,z)

Answer 4

x=r cos[theta]
y=r sin[theta]
z= z

Answer 5

I've come up with z = [(r^2)*(sin^2 theta - cos^2theta) + (2r)(sin theta + cos theta)]^1/2

Answer 6

look messy but I think It is right

Answer 7

cool thanks a bunch