A) \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2a(x+y+z)+2{{a}^{2}}=0\]
B) \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-2a(x+y+z)+2{{a}^{2}}=0\]
C) \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}\pm 2a(x+y+z)+2{{a}^{2}}=0\]
D) None of these
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 \[{{(x-a)}^{2}}+{{(y-b)}^{2}}+{{(z-c)}^{2}}={{r}^{2}}\], \[\therefore \] \[{{(x-a)}^{2}}+{{(y-a)}^{2}}+{{(z-a)}^{2}}={{a}^{2}}\] \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-2ax-2ay-2az+3{{a}^{2}}={{a}^{2}}\] \[\therefore \] \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-2a(x+y+z)+2{{a}^{2}}=0\] is the required equation of sphere.
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