Three Dimensional Geometry Question 24

Question: Under what condition does the equation $ x^{2}+y^{2}+z^{2}+2uc+2uy+2wz+d=0 $ represent a real sphere?

Options:

A) $ u^{2}+v^{2}+w^{2}=d^{2} $

B) $ u^{2}+v^{2}+w^{2}>d $

C) $ u^{2}+v^{2}+w^{2}<d $

D) $ u^{2}+v^{2}+w^{2}<d^{2} $

Show Answer

Answer:

Correct Answer: B

Solution:

[b] Equation $ x^{2}+y^{2}+z^{2}+2ux+2vy+2wz+d=0 $ Represent a real sphere if $ u^{2}+v^{2}+w^{2}>d $