Question

Equation $a{x}^2+b{y}^2+c{z}^2+2fyz+2gxz+2hxy+2ux+2vy+2wz+d=0$ represents a sphere, if

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

Answer 1

The correct option is D a=b=c and f=g=h=0

Equation of any sphere is in the form of $(x-a{)}^2+(y-b{)}^2+(c-z{)}^2=r^2$. On expanding it, we always see that the coefficients of $x^2$, $y^2$ and $z^2$ 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