Equation $\begin{matrix} a x^{2} + b y^{2} + c z^{2} + 2 f y z + 2 g x z + 2 h x y + 2 u x + 2 v y + 2 w z + d = 0 \end{matrix}$ represents a sphere, if
[MP PET 1990]

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If 'r' denotes the radius 'd' the distance of the origin from the centre of the sphere x2+y2+z2+2ux+2vy+2wz+4=0, then d2−r2 is

The correct option is B 4Given sphere is ,x2+y2+z2+2ux+2vy+2wz+4=0So, centre and radius of this sphere are C(u,v,w) and r=√u2+v2+w2−4Now, distance from origin to C is d=√u2+v2+w2Hence, d2−r2=4

If 'r' denotes the radius ' $d$ ' the distance of the origin from the centre of the sphere $x^{2} + y^{2} + z^{2} + 2 u x + 2 v y + 2 w z + 4 = 0$ , then $d^{2} - r^{2}$ is

The correct option is B $4$
Given sphere is , $x^{2} + y^{2} + z^{2} + 2 u x + 2 v y + 2 w z + 4 = 0$
So, centre and radius of this sphere are $C (u, v, w)$ and $r = \sqrt{u^{2} + v^{2} + w^{2} - 4}$
Now, distance from origin to $C$ is $d = \sqrt{u^{2} + v^{2} + w^{2}}$
Hence, $d^{2} - r^{2} = 4$