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The plane 6 x+k y+3 z-12=0 where meets the coordinate axes at A, B and C respectively. The equation of the sphere passing through the origin and A, B, C is x^2+y^2+z^2-2 x-3 y-4 z=0 . What is the value of k ?

Options

  1. A3
  2. B4
  3. C6
  4. D12

Correct answer

B. 4

Step-by-step solution

Since B (0, 12 k , 0 ) lies on sphere aligned & 0+ ( 12 k )^2+0-0-3 ( 12 k ) 0=0 & ( 12 k ) [ 12 k -3 ]=0 aligned aligned & 12 k -3=0[ k 0] & k =4 aligned

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