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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The equation x2+y2+z2+2ux+2vy+2wz+d=0 represents a sphere, if u2+v2+w2−d is

The correct option is B Positive or zeroThe expression u2+v2+w2−d represents (radius)2, hence this value has to be positive or atleast zero to get a real sphere.Hence, Option D is the correct option.

The equation $x^{2} + y^{2} + z^{2} + 2 u x + 2 v y + 2 w z + d = 0$ represents a sphere, if $u^{2} + v^{2} + w^{2} - d$ is

The correct option is B Positive or zero
The expression $u^{2} + v^{2} + w^{2} - d$ represents $(r a d i u s)^{2}$ , hence this value has to be positive or atleast zero to get a real sphere.
Hence, Option D is the correct option.