Home
Class 12
MATHS
A variable plane is at a constant distan...

A variable plane is at a constant distance 3r from the origin and meets the axes in A, B and C. Show that the locus of the centroid of the `Delta ABC` is `x^(-2) + y^(-2) + z^(-2) = r^(-2)`.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    SHARAM PUBLICATION|Exercise EXAMPLE|115 Videos

  • VECTORS

    SHARAM PUBLICATION|Exercise EXAMPLE|90 Videos

Similar Questions

Explore conceptually related problems

If tangents are drawn from the origin to the curve y = sin x, then show that the locus of the points of contact is x^(2) y^(2) = x^(2) - y^(2) .

A variable plane is at a constant distance p from the origin and meets the axes at A,B,C. Through A,B,C plane are drawn parallel to the co-ordinate planes. Show that the locus of their points of intersection is 1/x^2+1/y^2+1/z^2=1/p^2 .

If tangents are drawn from the origin to the curve y = sin x then show that the locus of the point of contact is x^2y^2 = x^2 - y^2 .

If the plane ax+by+cz=1 meets the co-ordinate axes at A,B,C, what is the centroid of the triangle ABC?

A variable plane meets the coordinate axes at A, B, C and is at a constant distance d from origin. Prove that the locus of the centroid of the triangle ABC is frac[1][x^2]+frac[1][y^2]+frac[1][z^2]=frac[9][d^2]

A sphere of constant radius k passes through the origin and meets the coordinate axes at P , Q , R . Prove that centroid of the triangle PQR lies on the sphere 9(x^(2)+y^(2)+z^(2)) = 4k^(2) .

A plane meets the co-ordinate axes at A,B,C such that the centroid of DeltaABC is (2,-2,3) . Find the equation of the plane.

A variable plane passes through a fixed point (a,b,c) and meets the co-ordinate axes at A,B,C. Show that the locus of the point common to the planes drawn through A,B and C parallel to the co-ordinate planes is a/x+b/y+c/z=1

SHARAM PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXAMPLE
  1. Find the equation of the plane Paralel to the plane 2x-y+3z+1=0 and at...

    Text Solution

    |

  2. Passing throughthe point (2,-3,1) and (-1,1-7) and perpendicular to th...

    Text Solution

    |

  3. Write the axis to which the plane by+cz+d=0 is parallal.

    Text Solution

    |

  4. Find the shortest distance between the lines (x-1)/(2) = (y-2)/(3) =...

    Text Solution

    |

  5. Find the equation of the plane which contains the line of intersection...

    Text Solution

    |

  6. Prove that the lines (x + 3)/(2) = (y + 5)/(3) = (z - 7)/(-3) and (x +...

    Text Solution

    |

  7. Prove that the four points (0, 4, 3), (-1, -5, -3), (-2, -2, 1) and (1...

    Text Solution

    |

  8. Find the distance from the line x/2 = y/3 = z/1 to the point (4, 5, 2)...

    Text Solution

    |

  9. A variable plane is at a constant distance 3r from the origin and meet...

    Text Solution

    |

  10. If the edges of a rectangular parallelopiped are of lengths a, b, c, t...

    Text Solution

    |

  11. If l1,m1,n1andl2,m2,n2 are the direction cosines of two mutually perpe...

    Text Solution

    |

  12. Find the image of the point (2, 3, 4) with respect to the plane x - y ...

    Text Solution

    |

  13. Prove that the two lines whose direction cosines are connected by the ...

    Text Solution

    |

  14. Find the equation of the plane through the points (2, 2,1)and (9, 3, 6...

    Text Solution

    |

  15. How far is the point (4, 1, 1) from the line of intersection of the pl...

    Text Solution

    |

  16. passing through the point (-1,3,2) perpendicular to the planes x+2y+...

    Text Solution

    |

  17. Find the point of intersection of the line (x-2)/3 = (y + 1)/4 = (z - ...

    Text Solution

    |

  18. Prove that the line joining (1,2,3),(2,1,-1) intersects the line joini...

    Text Solution

    |

  19. Find the equation of the line through the point (1, -2, 1) and paralle...

    Text Solution

    |

  20. Find the shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/...

    Text Solution

    |