• # question_answer If $(2,\,\,3,\,\,5)$ are ends of the diameter of a sphere${{x}^{2}}+{{y}^{2}}+{{z}^{2}}-6x$$-12y-2z+20=0$. Then coordinates of the other end are A) $(4,\,\,9,\,\,-3)$                            B) $(4,\,\,3,\,\,5)$C) $(4,\,\,3,\,\,-3)$                            D) $(4,\,\,-3,\,\,9)$

Solution :

Let the co-ordinate of other ends are$(x,\,\,y,\,\,z)$. The centre of sphere is$C(3,\,\,6,\,\,1)$. Therefore,$\frac{x+2}{2}=3\Rightarrow x=4$           $\frac{y+3}{2}=6\Rightarrow y=9$and$\frac{z+5}{2}=1\Rightarrow z=-3$

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