Question: The shortest distance from the plane $12 x + 4 y + 3 z = 327$to the sphere \(x ^ { 2 } + y ^ { 2 }...

Question

The shortest distance from the plane $12 x + 4 y + 3 z = 327$ to the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + 4 x - 2 y - 6 z = 155$ is

Answer 1

Centre of sphere is (–2, 1, 3)

Radius of sphere is $\sqrt { 4 + 1 + 9 + 155 } = 13$

Distance of centre from plane $= \frac { - 24 + 4 + 9 - 327 } { \sqrt { 144 + 16 + 9 } }$ $= \frac { 338 } { 13 }$

∴ Plane cuts the sphere and hence S.D. .

$= \frac { 338 } { 13 } - 13 = \frac { 169 } { 13 } = 13$ .

Question: The shortest distance from the plane \(12 x + 4 y + 3 z = 327\)to the sphere \(x ^ { 2 } + y ^ { 2 }...