The shortest distance from the origin to a variable point on the spher

1.	The shortest distance from the origin to a variable point on the sphere (x – 2)2 + (y – 3)2 + (z – 6)2 = 1 is (A) 5(B) 6(C) 7(D) 8
Answer» Correct option (B) 6 Explanation: Sphere x² + y² + z² – 4x – 6x – 12z + 48 = 0 Centre (2, 3, 6) radius = √(4 + 9 + 36 - 48) = 1 distance between centre and origin = √(4 + 9 + 36) = 7 shortest distance = 7 – 1 = 6 (Origin lies outside the sphere)

The shortest distance from the origin to a variable point on the sphere (x – 2)2 + (y – 3)2 + (z – 6)2 = 1 is (A) 5(B) 6(C) 7(D) 8

Answer»

Correct option (B) 6

Explanation:

Sphere x² + y² + z² – 4x – 6x – 12z + 48 = 0

Centre (2, 3, 6)

radius = √(4 + 9 + 36 - 48) = 1

distance between centre and origin = √(4 + 9 + 36) = 7

shortest distance = 7 – 1 = 6 (Origin lies outside the sphere)

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The shortest distance from the origin to a variable point on the sphere (x – 2)2 + (y – 3)2 + (z – 6)2 = 1 is (A) 5(B) 6(C) 7(D) 8

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