Consider the equation of a sphere x^2+y^2+z^2-4 x-6 y-8 z-16=0 . Which of the following statements is/are correct? 1. z -axis is tangent to the sphere. 2. The centre of the sphere lies on the plane x+y+z-9=0 . Select the correct answer using the code given below :

Step-by-step solution

aligned & x^2+y^2+z^2-4 x-6 y-8 z-16=0 & (x^2-4 x+4 )+ (y^2-6 y+9 )+ (z^2-8 z+16 ) & =16+4+9+16 & (x-2)^2+(y-3)^2+(z-4)^2=(3 5 )^2 & Centre of sphere =(2,3,4) & Radius =3 5 aligned Since, radius 3 5 is not equal to 2^2+3^2 = 13 Z -axis is not tangent to the sphere, so, statement 1 is wrong. 2+3+4-9=0 Centre of the sphere lies on the plane x+y+z-9=0 So, statement 2 is correct.