DẠNG 4. PHƯƠNG TRÌNH MẶT CẦU

\({(x - a)^2} + {(y - b)^2} + {(z + c)^2} = {R^2}.\)

\({(x - a)^2} + {(y + b)^2} + {(z - c)^2} = {R^2}.\)

\({(x + a)^2} + {(y + b)^2} + {(z + c)^2} = {R^2}.\)

\({(x - a)^2} + {(y - b)^2} + {(z - c)^2} = {R^2}.\)

\({(x + 5)^2} + {(y - 6)^2} + {(z + 7)^2} = 16\)

\({({\rm{x}} + 5)^2} + {({\rm{y}} - 6)^2} + {({\rm{z}} + 7)^2} = 4.\)

\({({\rm{x}} - 5)^2} + {({\rm{y}} + 6)^2} + {({\rm{z}} - 7)^2} = 4.\)

\({({\rm{x}} - 5)^2} + {({\rm{y}} + 6)^2} + {({\rm{z}} - 7)^2} = 16.\)

\({(x + 7)^2} + {(y - 8)^2} + {(z - 9)^2} = 9\)

\({(x + 7)^2} + {(y - 8)^2} + {(z - 9)^2} = 81.\)

\({({\rm{x}} + 7)^2} + {({\rm{y}} - 8)^2} + {({\rm{z}} - 9)^2} = 3.\)

\({(x - 7)^2} + {(y + 8)^2} + {(z + 9)^2} = 9.\)

\({\rm{I}}(1;2; - 5);{\rm{R}} = 4.\)

\({\rm{I}}(1;2; - 5);{\rm{R}} = 16.\)

\({\rm{I}}( - 1; - 2;5);{\rm{R}} = 4.\)

\({\rm{I}}( - 1; - 2;5);{\rm{R}} = 16.\)

\({\rm{I}}(1; - 2;3);{\rm{R}} = 25.\)

\({\rm{I}}(1; - 2;3);{\rm{R}} = 5.\)

\({\rm{I}}( - 1;2; - 3);{\rm{R}} = 5.\)

\({\rm{I}}( - 1;2; - 3);{\rm{R}} = 25.\)

\({x^2} + {y^2} + {z^2} - 4x - 2y + 5 = 0.\)

\({x^2} + {y^2} + {z^2} + 2x + 6y - 2z + 15 = 0.\)

\({x^2} + {y^2} + {z^2} - 4x + 1 = 0.\)

\({x^2} + {y^2} + {z^2} - 6z + 20 = 0.\)

\({({\rm{x}} - 1)^2} + {({\rm{y}} - 2)^2} + {({\rm{z}} - 3)^2} = 14.\)

\({(x + 1)^2} + {(y + 2)^2} + {(z + 3)^2} = 14.\)

\({({\rm{x}} - 1)^2} + {({\rm{y}} - 2)^2} + {({\rm{z}} - 3)^2} = 30.\)

\({({\rm{x}} + 1)^2} + {({\rm{y}} + 2)^2} + {({\rm{z}} + 3)^2} = 30.\)

\({({\rm{x}} - 1)^2} + {({\rm{y}} + 1)^2} + {({\rm{z}} - 4)^2} = 26.\)

\({(x + 1)^2} + {(y - 1)^2} + {(z - 4)^2} = 6.\)

\({({\rm{x}} - 1)^2} + {({\rm{y}} + 1)^2} + {({\rm{z}} - 4)^2} = 6.\)

\({({\rm{x}} + 1)^2} + {({\rm{y}} - 1)^2} + {({\rm{z}} - 4)^2} = 24.\)