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. $(-4,3,9)$

Answer 1

The correct option is A $(4,9,-3)$

Equation of sphere is
$x^2+y^2+z^2-6x-12y-2z+20=0$
whose coordinate of center are $(3,6,1)$.
Let the coordinate of the other end of diameter are $(\alpha ,\beta ,\gamma )$, then
$\frac{\alpha +2}{2}=3,\frac{\beta +3}{2}=6,\frac{\gamma +5}{2}=1$
Hence, $\alpha =4,\beta =9,\gamma =-3$
Thus, the coordinate of other point are $(4,9,-3)$.