A) \[\sqrt{3}\]
B) \[\sqrt{5}\]
C) \[\sqrt{7}\]
D) \[\sqrt{11}\]
Correct Answer: C
Solution :
The centre of the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-2y-4x-11=0\]is \[(0,1,2)\]and radius \[r=\sqrt{{{0}^{2}}+{{1}^{2}}+{{2}^{2}}+11}\] \[\Rightarrow \] \[r=OP=4\] Given equation of plane is \[x+2y+2z-15=0\] \[\therefore \]Distance from centre \[(0,1,2)\]to the plane, \[ON=\frac{|0+2+4-15|}{\sqrt{{{1}^{2}}+4+4}}=\frac{9}{3}=3\] In \[\Delta ONP,\] \[N{{P}^{2}}=O{{P}^{2}}-O{{N}^{2}}\] \[={{4}^{2}}-{{3}^{2}}\] \[=7\] \[\Rightarrow \] \[NP=\sqrt{7}\] \[\therefore \]Radius of the circle is \[\sqrt{7}.\]You need to login to perform this action.
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