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A sphere of constant radius 2k passes...

A sphere of constant radius `2k` passes through the origin and meets the axes in `A ,B ,a n dCdot` The locus of a centroid of the tetrahedron `O A B C` is a. `x^2+y^2+z^2=4k^2` b. `x^2+y^2+z^2=k^2` c. `2(k^2+y^2+z)^2=k^2` d. none of these

A

`x^(2)+y^(2)+z^(2)=4k^(2)`

B

`x^(2)+y^(2)+z^(2)=k^(2)`

C

`2(x^(2)+y^(2)+z^(2))=k^(2)`

D

none of these

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The correct Answer is:
B
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ML KHANNA-CO-ORDINATE GEOMETRY OF THREE DIMENSION-PROBLEM SET (4)
  1. The equation of the sphere circumscribing the tetrahedron whose faces ...

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  2. If a sphere of constant radius k passes through the origin and meets t...

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  3. The plane x/a+y/b+z/c=1 meets the coordinate axes at A,B and C respect...

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  4. A sphere of constant radius 2k passes through the origin and meets ...

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  5. The center of the sphere which passes through (a,0,0),(0,b,0),(0,0,c) ...

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  6. Find the equation of the sphere which passes through the point (1,0,0)...

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  7. The plane 2x-2y+z+12=0 touches the sphere x^(2)+y^(2)+z^(2)-2x-4y+2z-3...

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  8. The equation of the sphere concentric with the sphere x^(2)+y^(2)+z^(2...

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  9. Equation of the sphere with center (1,-1,1) and radius equal to that o...

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  10. If (2, 3, 5) is one end of a diameter of the sphere x^(2)+y^(2)+z^(2)-...

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  11. If (2, 3, 5) is one end of a diameter of the sphere x^(2)+y^(2)+z^(2)-...

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  12. Find the number of sphere of radius r touching the coordinate ax...

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  13. The radius of the circular section of the sphere x^(2)+y^(2)+z^(2)=25 ...

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  14. The radius of the circle in which the sphere x^(I2)+y^2+z^2+2z-2y-4...

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  15. The center of the circle x^(2)+y^(2)+z^(2)-3x+4y-2z-5=0 and 5x-2y +4...

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  16. The center of a sphere which touches the lines y=x,z=c and y=-x,z=-c l...

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  17. The shortest distance from the plane 12 x+y+3z=327 to the sphere x^...

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  18. The intersection of the spheres x^2+y^2+z^2+7x-2y-z=13a n dx^2+y^2=...

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  19. If the plane 2ax-3ay+4az+6=0 passes through the mid point of the line ...

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