Trong không gian với hệ trục tọa độ Oxyz, cho ba điểm A(1;2;-4), B(1;-3;1), C(2;2;3)

* Hướng dẫn giải

Chọn C

Gọi tâm mặt cầu là: I(x;y;0). 

$$\begin{gathered} \left\{\begin{array}{l}IA=IB\\ IA=IC\end{array}\iff \left\{\begin{array}{l}\sqrt{{(x-1)}^2+{(y-2)}^2+4^2}=\sqrt{{(x-1)}^2+{(y+3)}^2+1^2}\\ \sqrt{{(x-1)}^2+{(y-2)}^2+4^2}=\sqrt{{(x-2)}^2+{(y-2)}^2+3^2}\end{array}\right.\right. \\ \iff \left\{\begin{array}{l}{ (y-2)}^2+4^2={(y+3)}^2+1^2\\ x^2-2x+1+16=x^2-4x+4+9\end{array}\right.\iff \left\{\begin{array}{l}10y=10\\ 2x=-4\end{array}\right. \\ \iff \left\{\begin{array}{l}x=-2\\ y=1\end{array}\right. \\ \Rightarrow d=2R=2\sqrt{{(-3)}^2+{(-1)}^2+4^2}=2\sqrt{26} \end{gathered}$$