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 the coordinates of the other end of the diameter are-

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

Answer 1

Answer: (A)

(4, 9, -3)

Let other end be $(a,b,c)$

Using diameter form, we get

$(x-2)(x-a)+(y-3)(y-b)+(z-5)(z-c)=x^2+z^2+y^2-6x-12y-2z+20$

On comparing, we get

$2+a=6⟹a=4$

$3+b=12⟹b=9$

$5+c=2⟹c=-3$

So, other end will be $(4,9,-3)$