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

Answer 1

Answer: (C)

$(4,9,-3)$

Equation of the sphere is : $x^2+y^2+z^2-6x-12y-2z+20=0$

One end of the diameter is $A(2,3,5)$

Let us consider $(x,y,z)$ be the other end of the diameter

Center C = mid point of AB..

$\Rightarrow [\frac{2+x}{2},\frac{3+y}{2},\frac{5+z}{2}]=(3,6,1)$

$\therefore \frac{2+x}{2}=3$ $\Rightarrow 2+x=6$ $\Rightarrow x=4.$

$\Rightarrow \frac{3+y}{2}=6$ $\Rightarrow 3+y=12$ $\Rightarrow y=9.$

$\Rightarrow \frac{5+z}{2}=1$ $\Rightarrow 5+z=2$ $\Rightarrow z=-3.$

Other end of the diameter is $B(4,9,–3)$