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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 equation of the line through the origin and the centre of the sphere?

Options

  1. Ax=y=z
  2. B2 x=3 y=4 z
  3. C6 x=3 y=4 z
  4. D6 x=4 y=3 z

Correct answer

D. 6 x=4 y=3 z

Step-by-step solution

Equation of line passing through (0,0,0) and (1, 3 2 , 2 ) is x-0 1 = y-0 3 2 = z-0 2 6 x=4 y=3 z For question 94 and 95 Since point (2,3,-6) lies plane aligned & 2 x k + 2 y 3 + z 3 =2 & 4 k + 6 3 - 6 3 =2 & 4 k =2 k =2 aligned So, equation of plane is aligned & x+ 2 y 3 + z 3 =2 & 3 x+2 y+z=6 aligned

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