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Question

Equation ax2+by2+cz2+2fyz+2gxz+2hxy+2ux+2vy+2wz+d=0 represents a sphere, if

A
a=b=c
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B
f=g=h=0
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C
v=u=w
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D
a=b=c and f=g=h=0
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Solution

The correct option is D a=b=c and f=g=h=0
Equation of any sphere is in the form of (xa)2+(yb)2+(cz)2=r2. On expanding it, we always see that the coefficients of x2, y2 and z2 will always be the same and the xy, yz and zx terms don't exist.

Therefore from the question, a=b=c and f=g=h=0

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