The equation of sphere concentric with the sphere x2 + y2 + z2 - 4x - 6y - 8z - 5 = 0 and which passes through the origin, is

Question

The equation of sphere concentric with the sphere x2 + y2 + z2 - 4x - 6y - 8z - 5 = 0 and which passes through the origin, is (A) x2 + y2 + z2 - 4x - 6y - 8z = 0 (B) x2 + y2 + z2 - 6y - 8z = 0 (C) x2 + y2 + z2 = 0 (D) x2 + y2 + z2 - 4x - 6y - 8z - 6 = 0

Tardigrade Admin · Accepted Answer

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

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

$x^{2} + y^{2} + z^{2} - 4 x - 6 y - 8 z = 0$

$x^{2} + y^{2} + z^{2} - 6 y - 8 z = 0$

$x^{2} + y^{2} + z^{2} = 0$

$x^{2} + y^{2} + z^{2} - 4 x - 6 y - 8 z - 6 = 0$

Q. The equation of sphere concentric with the sphere x2+y2+z2−4x−6y−8z−5=0 and which passes through the origin, is

x2+y2+z2−4x−6y−8z=0

x2+y2+z2−6y−8z=0

x2+y2+z2=0

x2+y2+z2−4x−6y−8z−6=0

The equation of the sphere concentric with the sphere x2+y2+z2−4x−6y−8z−5=0 is x2+y2+z2−4x−6y−8z+c=0 ... (i) Since, this sphere Eq. (i) passes through origin, therefore 0+0+0−0−0−0+c=0 ⇒c=0 Hence, the required equation of sphere is x2+y2+z2−4x−6y−8z=0

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

$x^{2} + y^{2} + z^{2} - 4 x - 6 y - 8 z = 0$

$x^{2} + y^{2} + z^{2} - 6 y - 8 z = 0$

$x^{2} + y^{2} + z^{2} = 0$

$x^{2} + y^{2} + z^{2} - 4 x - 6 y - 8 z - 6 = 0$