Answer
Ans. Radius=√74
Coordinates of centre=(2, 1,-4)
Work Step by Step
Coordinates of diameter are A(1, -2, 4) and B (3, 4,-12)
Diameter AB=$\sqrt({x_2-x_1}^2)+({y_2-y_1}^2) +({z_2-z_1}^2) $
$\sqrt({3-1}^2)+({4+2}^2) +({-12-4}^2) $
$\sqrt({x_2-x_1}^2)+({y_2-y_1}^2) +({z_2-z_1}^2) $
$\sqrt({4}^2)+({6}^2) +({-16}^2) $
$\sqrt4+36 +256 $
$\sqrt296$
$\sqrt{74}×2$
Radius=$\sqrt{74}×2$/2=√74
Centre of circle:- here o is centre of circle
Let coordinates of centre be (g, h, f)
g=$\frac{1+3}{2}$=2 h$\frac{-2+4}{2}$=1 f=$\frac{4-12}{2}$=-4
g, h, f=(2, 1,-4)
