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Câu hỏi: Trong không gian $Oxyz$, phương trình mặt cầu có tâm $I\left( 1;-4;3 \right)$, bán kính $R=3\sqrt{2}$ là
A. ${{\left( x-1 \right)}^{2}}+{{\left( y+4 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=3\sqrt{2}$.
B. ${{\left( x-1 \right)}^{2}}+{{\left( y+4 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=18$.
C. ${{\left( x-1 \right)}^{2}}+{{\left( y-4 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=18$.
D. ${{\left( x+1 \right)}^{2}}+{{\left( y-4 \right)}^{2}}+{{\left( z+3 \right)}^{2}}=18$
A. ${{\left( x-1 \right)}^{2}}+{{\left( y+4 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=3\sqrt{2}$.
B. ${{\left( x-1 \right)}^{2}}+{{\left( y+4 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=18$.
C. ${{\left( x-1 \right)}^{2}}+{{\left( y-4 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=18$.
D. ${{\left( x+1 \right)}^{2}}+{{\left( y-4 \right)}^{2}}+{{\left( z+3 \right)}^{2}}=18$
Phương trình mặt cầu là:
${{\left( x-1 \right)}^{2}}+{{\left( y+4 \right)}^{2}}+{{\left( z-3 \right)}^{2}}={{\left( 3\sqrt{2} \right)}^{2}}$ $\Leftrightarrow $ ${{\left( x-1 \right)}^{2}}+{{\left( y+4 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=18$.
${{\left( x-1 \right)}^{2}}+{{\left( y+4 \right)}^{2}}+{{\left( z-3 \right)}^{2}}={{\left( 3\sqrt{2} \right)}^{2}}$ $\Leftrightarrow $ ${{\left( x-1 \right)}^{2}}+{{\left( y+4 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=18$.
Đáp án B.