Question

The equation of a sphere is $x^2+y^2+z^2-10z=0$. If one end point of a diameter of the sphere is (- 3, - 4, 5), what is the other end point ?

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

Answer 1

Answer: (B)

The equation of the given sphere is
$x^2+y^2+z^2-10z=0.$
$\therefore$ Its centre is $\left(0,0,5\right)$.
Coordinates of one end point of a diameter of the sphere is given as $\left(-3,-4,5\right)$.
Let Coordinates of another end point of this diameter $\left(x_1,y_1,z_1\right)$
$\therefore \frac{-3+x_1}{2}=0\Rightarrow x_1=3$
$\frac{-4+y_1}{2}=0\Rightarrow y_1=4$
and $\frac{5+z_1}{2}=5\Rightarrow z_1=5$
$\therefore$ Required coordinates are $\left(3,4,5\right).$