The equation ax^2 + by^2 + cz^2 + 2fyz + 2gxz | vedclass

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(D) The general second-degree equation in three variables is given by $ax^2 + by^2 + cz^2 + 2fyz + 2gxz + 2hxy + 2ux + 2vy + 2wz + d = 0$. For this eq

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

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(D) The general second-degree equation in three variables is given by $ax^2 + by^2 + cz^2 + 2fyz + 2gxz + 2hxy + 2ux + 2vy + 2wz + d = 0$. For this equation to represent a sphere,the coefficients of the squared terms must be equal,i.e.,$a = b = c 
eq 0$. Additionally,there should be no product terms of the variables (like $xy$,$yz$,or $zx$),which implies that the coefficients of these terms must be zero,i.e.,$f = g = h = 0$. Therefore,the conditions are $a = b = c$ and $f = g = h = 0$.

The equation $ax^2 + by^2 + cz^2 + 2fyz + 2gxz + 2hxy + 2ux + 2vy + 2wz + d = 0$ represents a sphere,if:

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