question_answer

The shortest distance from the plane \[12x+4y+3z=327\] to the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+4x-2y-6z=155\] is     AIEEE  Solved  Paper-2003

A) 26          

B)       \[11\frac{4}{13}\]                            

C)       13      

D)       39

Correct Answer: C

Solution :

                Equations of sphere and plane are                     and            Centre of the sphere is (- 2, 1, 3) and radius of sphere                                     Length of the perpendicular from centre on the plane         Shortest distance between the plane and sphere = 26 - Radius of sphere = 26 ? 13 = 13