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)
• E. (4,9,5)

Answer 1

The correct option is B (4,9,-3)

Equation of sphere is, $x^2+y^2+z^2-6x-12y-2z+20=0$
Centre of sphere = (3,6,1) and one end of circle = (2,3,5)
Let other end be (x,y,z)
$\therefore \frac{2+x}{2}=3,\frac{3+y}{2}=6,\frac{5+z}{2}=1$
$\Rightarrow$ x=6-2, y=12-3, z=2-5
$\Rightarrow$ x=4, y=9, z=-3
Hence, other end is (4,9,-3)