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Question

The shortest distance from the plane 12x + 4y + 3z = 327 to the sphere x2+y2+z2+4x2y6z=155 is


A
1134
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B
13
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C
39
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D
26
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Solution

The correct option is B 13
The centre of the sphere is (-2, 1, 3) and its radius is 4+1+9+155=13.
Length of the perpendicular from the centre of the sphere on the plane is 24+4+9327144+16+9=33813=26
So the plane is outside the sphere and the required distance is equal to 26 - 13 = 13.

Mathematics

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