Final answer:
The equation of the set of all points equidistant from s=(-1,2,-5) is (x+1)^2 + (y-2)^2 + (z+5)^2 = d^2.
Step-by-step explanation:
The set of points equidistant from a given point is called a sphere.
Given the point s=(-1,2,-5), we can find the equation of the sphere by using the distance formula.
The distance between any point (x,y,z) on the sphere and the point s=(-1,2,-5) should be the same.
So, using the distance formula, we get: √((x-(-1))^2 + (y-2)^2 + (z-(-5))^2) = d, where d is the distance.
Squaring both sides of the equation and expanding, we get: (x+1)^2 + (y-2)^2 + (z+5)^2 = d^2.