Equation Vbeginmatrixa 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-0lend matrix represents a sphere- if -MP PET 1990-

The correct option is A a = b = c and f = g = h = 0It is obvious. ...

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Equation Vbeg...

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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]

a = b = c

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f = g = h = 0

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v = u = w

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a = b = c and f = g = h = 0

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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

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

a x^{2} + a y^{2} + a z^{2} + 2 u x + 2 v y

+ 2 w z + d = 0, a \neq 0

x^{2} + y^{2} + z^{2} + 2 u x + 2 v y + 2 w z + d = 0

u^{2} + v^{2} + w^{2} - d

d

x^{2} + y^{2} + z^{2} + 2 u x + 2 v y + 2 w z + 4 = 0

d^{2} - r^{2}

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