Question

Find an equation of the sphere that has center (2,3,-1) and contains the point (1,7,-9)

Answer 1

The equation of the sphere is

$$(x-2)^2+(y-3)^2+(z+1)^2=R^2$$

The sphere contains the point $(1,7,-9)$

$$(1-2)^2+(7-3)^2+(-9+1)^2=81$$

The equation of the sphere that has center $(2,3,-1)$ and contains the point $(1,7,-9)$

$$(x-2)^2+(y-3)^2+(z+1)^2=81$$