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Câu hỏi: Viết phương trình mặt cầu tâm $I\left( 1; 2; 3 \right)$ và tiếp xúc với $\left( Oyz \right)$ ?
A. ${{\left( x-1 \right)}^{2}}+{{\left( y-2 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=4.$
B. ${{\left( x-1 \right)}^{2}}+{{\left( y-2 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=1.$
C. ${{\left( x-1 \right)}^{2}}+{{\left( y-2 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=9.$
D. ${{\left( x-1 \right)}^{2}}+{{\left( y-2 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=25.$
A. ${{\left( x-1 \right)}^{2}}+{{\left( y-2 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=4.$
B. ${{\left( x-1 \right)}^{2}}+{{\left( y-2 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=1.$
C. ${{\left( x-1 \right)}^{2}}+{{\left( y-2 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=9.$
D. ${{\left( x-1 \right)}^{2}}+{{\left( y-2 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=25.$
Do mặt cầu tiếp xúc với $\left( Oyz \right)$ nên ta có $R=d\left[ I,\left( Oyz \right) \right]=\left| {{x}_{I}} \right|=1$
$\Rightarrow \left( S \right):{{\left( x-1 \right)}^{2}}+{{\left( y-2 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=1$
$\Rightarrow \left( S \right):{{\left( x-1 \right)}^{2}}+{{\left( y-2 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=1$
Đáp án B.