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If plane 2x+3y+6z+k=0 is tangent to the ...

If plane `2x+3y+6z+k=0` is tangent to the sphere `x^(2)+y^(2)+z^(2)+2x-2y+2z-6=0`, then a value of k is

A

26

B

16

C

`-26`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Center and radius of the sphere are `(-1,1,-1)` and 3, respectively.
Distance of `(-1,1,-1)` from the plane is `|(-2+3-6+k)/sqrt(4+9+36)|`.
Since, the plane is tangent to the plane.
`therefore |(k-5)/7|=3`.
`therefore k=-16,26`
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