A) \[9{{x}^{2}}-25{{y}^{2}}+25{{z}^{2}}=225\]
B) \[9{{x}^{2}}+25{{y}^{2}}-25{{z}^{2}}=225\]
C) \[9{{x}^{2}}+25{{y}^{2}}+25{{z}^{2}}=225\]
D) \[9{{x}^{2}}+25{{y}^{2}}+25{{z}^{2}}+225=0\]
Correct Answer: C
Solution :
\[\sqrt{{{(x-4)}^{2}}+{{y}^{2}}+{{z}^{2}}}+\sqrt{{{(x+4)}^{2}}+{{y}^{2}}+{{z}^{2}}}=10\] \[\Rightarrow \,\,2\,({{x}^{2}}+{{y}^{2}}+{{z}^{2}})+2\sqrt{[{{(x-4)}^{2}}+{{y}^{2}}+{{z}^{2}}]\,[{{(x+4)}^{2}}+{{y}^{2}}+{{z}^{2}}]}\] \[=100-32=68\] \[\Rightarrow \,\,{{({{x}^{2}}+{{y}^{2}}+{{z}^{2}}-34)}^{2}}\] \[=[{{(x-4)}^{2}}+{{y}^{2}}+{{z}^{2}}]\,[{{(x+4)}^{2}}+{{y}^{2}}+{{z}^{2}}]\] \[\Rightarrow \,\,{{({{x}^{2}}+{{y}^{2}}+{{z}^{2}})}^{2}}-68\,({{x}^{2}}+{{y}^{2}}+{{z}^{2}})+{{(34)}^{2}}\] \[=[({{x}^{2}}+{{y}^{2}}+{{z}^{2}}+16)-8x]\,\,[({{x}^{2}}+{{y}^{2}}+{{z}^{2}}+16)+8x]\] \[={{({{x}^{2}}+{{y}^{2}}+{{z}^{2}}+16)}^{2}}-64{{x}^{2}}\] \[=\,({{x}^{2}}+{{y}^{2}}+{{z}^{2}})+32\,({{x}^{2}}+{{y}^{2}}+{{z}^{2}})-64{{x}^{2}}+{{(16)}^{2}}\] \[\Rightarrow \,\,9{{x}^{2}}+25{{y}^{2}}+25{{z}^{2}}-225=0\].
You need to login to perform this action.
You will be redirected in
3 sec
