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Q. The equation of sphere concentric with the sphere $x^2 + y^2 + z^2 - 4x - 6y - 8z - 5 = 0$ and which passes through the origin, is

VITEEEVITEEE 2010Three Dimensional Geometry

Solution:

The equation of the sphere concentric with the sphere
$x^{2}+y^{2}+z^{2}-4 x-6 y-8 z-5=0$ is
$x^{2}+y^{2}+z^{2}-4 x-6 y-8 z+ c=0$ ... (i)
Since, this sphere Eq. (i) passes through origin, therefore
$0+0+0-0-0-0+c=0$
$\Rightarrow c=0$
Hence, the required equation of sphere is
$x^{2}+y^{2}+z^{2}-4 x-6 y-8 z=0$