Given: The centre of the sphere is (1, 1, 2) and it passes through the point (2, 4, 6). Let the radius be R As we know that , equation of a sphere cantered at the poin (x0,y0,z0) with radius R is given by (x−x0)2+(y−y0)2+(z−z0)2=R2 Here x0=1,y0=1,z0=2 So, the equation of sphere is: (x−1)2+(y−1)2+(z−2)2=R2 It is given that the sphere passes through the point (2,4,6) i.e The point point (2,4,6) will satisfy the equation (x−1)2+(y−1)2+(z−2)2=R2 ⇒(2−1)2+(4−1)2+(6−2)2=R2 ⇒R2=26 ⇒(x−1)2+(y−1)2+(z−2)2=26 ⇒x2+y2+z2−2x−2y−4z−20=0 Hence, the equation of the required sphere is: x2+y2+z2−2x−2y−4z−20=0