NDA 2 2025 Maths, question 54

Topic: Analytical geometry

Passage · Q53 to Q54

Suppose $S$ is the sphere with the smallest radius that passes through the points $A(1,0,0)$ , $B(0,1,0)$ and $C(0,0,1)$ .

Q54

On which one of the following planes does the centre of $S$ lie?

(a) $x+y+z-1=0$ Correct answer
(b) $x+y+z+1=0$
(c) $3x+3y+3z-1=0$
(d) $3x+3y+3z+1=0$

Solution.

Answer: (a) $x+y+z-1=0$

The minimum-radius centre is (1/3,1/3,1/3), whose coordinate sum is 1.
It therefore lies on x+y+z−1=0.
Substitution rules out the other three planes.