The correct option is B x2+y2+z2−2x+4y−6z+10=0
Equation of a sphere through given circle is
(x2+y2+z2+7y−2z+2)+λ(2x+3y+4z−8)=0.
Its centre is (−λ,−7+3λ2,−4λ−22).
If the given circle is a great circle, then the plane 2x+3y+4z−8=0 passes through centre.
∴−2λ−32(7+3λ)−2(4λ−2)−8=0.
∴(−2−92−8)λ−212+4−8=0,
∴29λ2+292=0;
∴λ=−1.
Putting λ=−1, we get the equation of sphere as
x2+y2+z2−2x+4y−6z+10=0