If the center of the sphere ax2+by2+cz2−2x+4y+2z−3=0is (1/2,−1,−1/2), what is the value of b ?

[c] The given equation of sphere is ax2+by2+cz2−2x+4y+2z−3=0 This equation represents a equation of sphere, if coefficient of x2,y2 and z2 is same. i.e., a =b =c ∴ Equation of sphere can be re-written as bx2+by2+bz2−2x+4y+2z−3=0 ⇒x2+y2+Z2−2xb+4yb+2zb−3b=0 The centre of this sphere is (1b,−2b,−1b) Given that the centre of sphere is (12,−1,−1b) 1b=12⇒b=2