JEE Main · 2007 · 29 Apr 2007 · Offline · Three Dimensional Geometry

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(2, 3, 5)

is one end of a diameter of the sphere

x^{2} + y^{2} + z^{2} - 6 x - 12 y - 2 z + 20 = 0

, then the coordinates of the other end of the diameter are

(A) $(4, 9, - 3)$ ✓ Correct
(B) $(4, - 3, 3)$
(C) $(4, 3, 5)$
(D) $(4, 3, - 3)$

Answer: (A)

Solution

Completing the squares shows the sphere has centre

(3, 6, 1)

. The centre is the midpoint of any diameter, so with one end at

(2, 3, 5)

the other end

(α, β, γ)

satisfies

\frac{α + 2}{2} = 3

\frac{β + 3}{2} = 6

and

\frac{γ + 5}{2} = 1

. Solving these gives the other end as

(4, 9, - 3)

JEE Main · 2007 · 29 Apr 2007 · Offline · Single correct option

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