Discussion Forum

If (2,7,3)  is one end of a diameter of the sphere x²+y²+z²-6x-12y-2z+20=0, then the coordinate of the other end of the diameter  are 

Answer:

Explanation:

Given sphere is  x²+y²+z²-6x-12y-2z+20=0, Centre =(3,6,1)

 Here, one end of diameter is (2,7,3) , let the other end of the diameter be (x,y,z)

Centre of the sphere will be the mid-point of the ends of diameter.

 So, (3,6,1)=   $\left(\frac{2+x}{2},\frac{7+y}{2}, \frac{3+z}{2}\right)$

 $\Rightarrow 2+x=6\Rightarrow x=4$

$\Rightarrow 7+y=12\Rightarrow y=5$   and  $\Rightarrow 3+z=2\Rightarrow z=-1$

 Therefore     (x,y,z) =(4,5,-1)