Question

Find the standard equation of the sphere with the given characteristics. Center: (-1, -7,3) Radi Radius: S

Answer 1

Is that a radius of S instead of a number?  

The sphere consists of the points equidistant from the center.  So by the Pythagorean Theorem (applied twice) that's

$(x + 1)^2 - (y+7)^2+(z-3)^2 = S^2$