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