Answer
The required equation in cylindrical form:- z=r$\sqrt cos2θ$
The required equation in spherical form:-cotΦ=√cos2θ
Work Step by Step
Given :- z=$\sqrt {x^2-y^2}$
The co-ordinate of equation in in cylindrical form
x=rcosθ y=rsinθ
Solve the equation in cylindrical form can be written
z=$\sqrt {(rcosθ) ^2-(rsinθ)^2}$
Z=r$\sqrt cos2θ$
Co-ordinate of equation in is spherical form
x=rcosθsinΦ y=rsinθsinΦ
Z= ρcosΦ
ρcosΦ=$\sqrt {(rcosθsinΦ) ^2-(rsinθsinΦ)^2}$
ρcosΦ=$\sqrt {( ρsinΦ) ^2(cos2θ)}$
CotΦ=√cos2θ ans.
