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Giải bài tập 5.38 trang 62 SGK Toán 12 tập 2 - Kết nối tri thức

Trong không gian Oxyz, cho mặt cầu (S): \({\left( {x + 1} \right)^2} + {y^2} + {\left( {z - 3} \right)^2} = 4\). Tọa độ tâm I và bán kính R của (S) lần lượt là A. \(I\left( {1;0;3} \right),R = 4\). B. \(I\left( {1;0;3} \right),R = 2\). C. \(I\left( { - 1;0;3} \right),R = 2\). D. \(I\left( { - 1;0;3} \right),R = 4\).

Tổng hợp đề thi học kì 2 l꧋ớp 12 tất cả các môn -🍨 Kết nối tri thức

Toán - Văn - Anh - Hoá - Sinh - Sử - Địa
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Đề bài

Trong không gian Oxyz, cho mặt cầu (S): \({\left( {x + 1} \right)^2} + {y^2} + {\left( {z - 3} \right)^2} = 4\). Tọa độ tâm I và bán kính R của (S) lần lượt là A. \(I\left( {1;0;3} \right),R = 4\). B. \(I\left( {1;0;3} \right),R = 2\). C. \(I\left( { - 1;0;3} \right),R = 2\). D. \(I\left( { - 1;0;3} \right),R = 4\).

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về phương trình mặt cầu để chứng minh: Trong không gian Oxyz, mặt cầu (S) tâm \(I\left( {a;b;c} \right)\), bán kính R có phương trình \({\left( {x - a} \right)^2} + {\left( {y - b} \right)^2} + {\left( {z - c} \right)^2} = {R^2}\).

Lời giải chi tiết

Ta viết lại phương trình mặt cầu (S) được: \({\left[ {x - \left( { - 1} \right)} \right]^2} + {\left( {y - 0} \right)^2} + {\left( {z - 3} \right)^2} = {2^2}\) Mặt cầu (S) có tâm \(I\left( { - 1;0;3} \right),\) bán kính \(R = 2\). Chọn C

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