Question
Passage: The equation of the sphere S is x^2+y^2+z^2-4x-6y-12z+k=0. Question: If the radius of the sphere S is 8 units, what is the value of k ?
NDA
Mathematics
Three Dimensional Geometry
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. -15
- B. 7
- C. 10
- D. 15
Answer
A. -15
Step-by-step solution
The given equation of the sphere is x^2+y^2+z^2-4x-6y-12z+k=0. Comparing this with the general equation of a sphere x^2+y^2+z^2+2ux+2vy+2wz+d=0, we get: u = -2, v = -3, w = -6, and d = k. The radius of the sphere is given by r = u^2+v^2+w^2-d . Substituting the given values: 8 = (-2)^2+(-3)^2+(-6)^2-k 8 = 4+9+36-k 8 = 49-k Squaring both sides: 64 = 49-k k = 49-64 = -15 Answer: -15
Related: Mathematics — Three Dimensional Geometry · All PYQ Banks