Home
Class 12
MATHS
A variable plane is at a distance, k fro...

A variable plane is at a distance, k from the origin and meets the coordinates axis in A, B , C. Then, the locus of the centroid of `triangleABC` is

A

`x^(-2)+y^(-2)+z^(-2)=(16)`

B

`x^(-2)+y^(-2)+z^(-2)=9`

C

`(1)/(9)((1)/(x^2+(1)/(y^2)+(1)/(z^2)))=0`

D

`X+Y=0`

Text Solution

Verified by Experts

The correct Answer is:
(b,c)
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|12 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise Exercise (Passage Based Questions)|33 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Option Correct Type Questions)|96 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

A variable plane is at a distance k from the origin and meets the coordinates axes is A,B,C. Then the locus of the centroid of DeltaABC is

A variable plane is at a constant distance p from the origin and meets the coordinate axes in A , B , C . Show that the locus of the centroid of the tetrahedron O A B C is x^(-2)+y^(-2)+z^(-2)=16p^(-2)

A variable plane is at a constant distance p from the origin and meets the coordinate axes in A , B , C . Show that the locus of the centroid of the tehrahedron O A B Ci sx^(-2)+y^(-2)+z^(-2)=16p^(-2)dot

If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A,B anc C, then the locus of the centroid of Delta ABC is :

A variable plane which remains at a constant distance p from the origin cuts the coordinate axes in A, B, C. The locus of the centroid of the tetrahedron OABC is x^(2)y^(2)+y^(2)z^(2)+z^(2)x^(2)=(k)/(p^(2))x^(2)y^(2)z^(2), then root(5)(2k) is

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A, B, C. Show that the locus of the centroid of triangle ABC is x^(-2) + y^(-2) + z^(-2) = p^(-2) .

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A, B, C. Show that the locus of the centroid of triangle ABC is 1/x^2+1/y^2+1/z^2=1/p^2 .

A variable plane at constant distance p form the origin meets the coordinate axes at P,Q, and R. Find the locus of the point of intersection of planes drawn through P,Q, r and parallel to the coordinate planes.

A circle of radius r passes through the origin and meets the axes at A and B. The locus of the centroid of triangleOAB" is"

A variable plane at a constant distance p from the origin meets the coordinate axes in points A,B and C respectively.Through these points , planes are drawn parallel to the coordinate planes, show that locus of the point of intersection is 1/x^2+1/y^2+1/z^2=1/p^2

ARIHANT MATHS ENGLISH-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (More Than One Correct Option Type Questions)
  1. Which of the following statements is/are correct?

    Text Solution

    |

  2. Which of the following is/are correct about a tetrahedron?

    Text Solution

    |

  3. A variable plane is at a distance, k from the origin and meets the coo...

    Text Solution

    |

  4. Equation of any plane containing the line (x-x1)/(a)=(y-y1)/(b)=(z-z1)...

    Text Solution

    |

  5. The line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the curve x^2+y^2=r...

    Text Solution

    |

  6. A vector equally inclined to the vectors hat(i)-hat(j)+hat(k) and hat(...

    Text Solution

    |

  7. Consider the plane through (2, 3, -1) and at right angles to the vecto...

    Text Solution

    |

  8. A plane passes through a fixed point (a, b, c) and direction ratios of...

    Text Solution

    |

  9. Let A be vector parallel to line of intersection of planes P1 and P2. ...

    Text Solution

    |

  10. Find the angle between the planes 2x+y+z-1=0 and 3x+y+2z-2=0,

    Text Solution

    |

  11. Find the direction ratios of this plane 2x-3y+4z+2=0

    Text Solution

    |

  12. A line segment has length 63 and direction ratios are 3,-2 and 6. The ...

    Text Solution

    |

  13. The lines (x-2)/(1)=(y-3)/(1)=(z-4)/(-k) and (x-1)/(k)=(y-4)/(2)=(z-5)...

    Text Solution

    |

  14. The points A(4, 5, 10), B(2, 3, 4) and C(1, 2, -1) are three vertices ...

    Text Solution

    |

  15. The lines x=y=z meets the plane x+y+z=1 at the point P and the sphere ...

    Text Solution

    |

  16. A rod of length 2units whose one end is (1, 0, -1) and other end touch...

    Text Solution

    |

  17. Consider the planes 2x+y+z+4=0, and y-z+4=0 Find the angle between the...

    Text Solution

    |

  18. The volume of a right triangular prism ABCA(1)B(1)C(1) is equal to 3 c...

    Text Solution

    |

  19. Let a plane pass through origin and be parallel to the line (x-1)/2=(y...

    Text Solution

    |

  20. Let OABC be a regular tetrahedron with side length unity, then its vol...

    Text Solution

    |