Question

If (2, 3, 5) is one end of a diameter of the sphere $x^{2} + y^{2} + z^{2} - 6x - 12y - 2z + 20 = 0$then co-ordinates of the other end of the diameter are

• A. (4, 3, 5)
• B. (4, 9, –3)
• C. (4, 9, 3)
• D. (4, 3, –3) (5) (4, 9, 5)

Answer 1

Answer: (B)

(4, 9, –3)

Answer 2

Equation of sphere is, $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 6 x - 12 y - 2 z + 20 = 0$

Centre of sphere $= ( 3,6,1 )$and one end of circle = $( 2,3,5 )$

Let other end be $( x , y , z )$

$\therefore$

⇒ $x = 6 - 2$, $y = 12 - 3$, $z = 2 - 5$

⇒ $x = 4 , y = 9 , z = - 3$

Hence, other end is (4, 9, –3).