(f) (i) Change x^2 - y^2 = 2y to polar equation. Leave your final answer in terms of sin  only. [4] (ii) Change (-1; 2; 2) to spherical coordinates.

Question

f) (i) Change x^2 - y^2 = 2y to polar equation. Leave your final answer in terms of sin  only. [4]

(ii) Change (-1; 2; 2) to spherical coordinates.

Answer 1

x^2 -y^2 =2y

x=rcosT, y=rsinT

r^2(cos^2T - sin^2T)= rsinT

r^2(1-2sin^2T)=rsinT

or

r=0

and

r-2rsinT=sinT

it's a hyperbola