Question

пожалуйста. добрые люди. . . . . . . .​

Answer 1

$\displaystyle\bf\\E(1 \ ; \ 0 \ ; \ -2) \ \ , \ R=\sqrt{6}$

Уравнение сферы имеет вид :

$\displaystyle\bf\\(x-x_{0})^{2} +( y-y_{0} )^{2} +(z-z_{0} )^{2} =R^{2} \\\\Otvet:(x-1)^{2}+y^{2} +(z+2)^{2} =6 \\\\\\2)\\\\O(0 \ ; \ -4 \ ; \ 9) \ \ , \ \ M(6 \ ; \ -1 \ ; \ 0)\\\\\\x^{2} +(y+4)^{2} +(z-9)^{2} =R^{2} \\\\6^{2} +(-1+4)^{2} +(0-9)^{2} =R^{2} \\\\36+9+81=R^{2} \\\\R^{2} =126\\\\Otvet:x^{2} +(y+4)x^{2} +(z-9)^{2} =126$

$\displaystyle\bf\\3)\\\\x^{2} +y^{2} +z^{2} +2y-4z=4\\\\x^{2} +(y^{2}+2y+1)+(z^{2} -4z+4) -1-4=4\\\\x^{2} +(y+1)^{2} +(z-2)^{2} =9$

Координаты центра (0 ; - 1 ; 2)  ,  R = 3