Three Dimensional Geometry Question 27
Question: The equation of the sphere touching the three co-ordinate planes is
[AMU 2002]
Options:
A) $ x^{2}+y^{2}+z^{2}+2a(x+y+z)+2a^{2}=0 $
B) $ x^{2}+y^{2}+z^{2}-2a(x+y+z)+2a^{2}=0 $
C) $ x^{2}+y^{2}+z^{2}\pm 2a(x+y+z)+2a^{2}=0 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Given, sphere touching the three co-ordinates planes. So clearly the center is $ (a,,a,,a) $ and radius is a. From $ {{(x-a)}^{2}}+{{(y-b)}^{2}}+{{(z-c)}^{2}}=r^{2} $ ,
$ \therefore $ $ {{(x-a)}^{2}}+{{(y-a)}^{2}}+{{(z-a)}^{2}}=a^{2} $ $ x^{2}+y^{2}+z^{2}-2ax-2ay-2az+3a^{2}=a^{2} $
$ \therefore $ $ x^{2}+y^{2}+z^{2}-2a(x+y+z)+2a^{2}=0 $ is the required equation of sphere.
BETA
