Answer
The required equation in cylindrical form:-z=$\sqrt {r^2-1}$
The required equation in spherical form:-cos2$\phi$=-1/$\rho^2$
Work Step by Step
Given:-z=$\sqrt {x^2+y^2-1}$
For finding the equation in cylindrical form
The co-ordinate of equation in cylindrical form
x=rcosθ y=rsinθ
z=$\sqrt {(rcosθ)^2+(rsinθ)^2-1}$
z=$\sqrt {r^2-1}$
For finding the equation in spherical form
The co-ordinate of equation in spherical form
z=$\rho$cos$\phi$
x=$\rho$cos$\theta$sin$\phi$
Y=$\rho$sin$\theta$sin$\phi$
z=$\sqrt {(ρcosθsinΦ)^2+(ρsinθsinΦ)^2-1}$
$\rho$cos$\phi$=$\sqrt {(ρcosθsinΦ)^2+(ρsinθsinΦ)^2-1}$
($\rho$cos$\phi$)^2=(ρsinΦ)^2-1
After solving we get
cos2$\phi$=-1/$\rho^2$
