KVPY SX SB Exam 2015 Question Paper

Question : 6 of 120

Marks: +1, -0

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

(x - 2)^2 + (y- 3)^2 + (z - 6)^2 = 1

is -

Solution:

Sphere

x^2 + y^2 + z^2-4x

- 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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