Passage: The equation of the sphere S is x^2+y^2+z^2-4x-6y-12z+k=0 . Question: What is the radius of the sphere passing through origin and concentric with the sphere S ?

Step-by-step solution

The equation of the given sphere is x^2+y^2+z^2-4x-6y-12z+k=0 . The center of the sphere is (2, 3, 6) . The required sphere is concentric with the given sphere, so its center is also (2, 3, 6) . Since the required sphere passes through the origin (0, 0, 0) , its radius is the distance between the center and the origin. R = (2-0)^2 + (3-0)^2 + (6-0)^2 R = 4 + 9 + 36 = 49 = 7 Answer: 7