Home
Class 12
MATHS
A variable plane meets the coordinate ax...

A variable plane meets the coordinate axes at P, Q, R points. If the plane passes through a fixed point (a, b, c), prove that the centre of the shpere passing the origin and P, Q, R will lie on the surface `a/x+b/y+c/z=2`

Promotional Banner

Topper's Solved these Questions

  • TEST PAPER 9

    MODERN PUBLICATION|Exercise EXERCISE|37 Videos

  • VECTOR

    MODERN PUBLICATION|Exercise EXERCISE|46 Videos

Similar Questions

Explore conceptually related problems

A plane meets the coordinate axes at A, B and C respectivély. If the centroid of the triangle ABC is (-1, 2, 5) then find the equation of the plane.

Write the equation of the plane passing through the point (3, 1, 2) and parallel to the plane 2x + 2y + 2z + 1= 0.

find the equation to the plane passing through the line x=y=z and the point (-1,3,4).

Find the equation of the plane passing through the line x = y = z and the point (3,2,1).

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.

Write the equation of the plane passing through the point(1,-2,3)and perpendicular to the y-axis.

Write the equation of the plane passing through (1,2,3) and parllel to the plane x+2y+5z=0 .

MODERN PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the equation of the plane passing through the line of intersectio...

    Text Solution

    |

  2. Find the equation of the plane .Passing through the point (2,3-1) and ...

    Text Solution

    |

  3. Bisecting the line segment joining (-1,4,3) and (5,-2,-1) at right ang...

    Text Solution

    |

  4. Find the equation of the plane Paralel to the plane 2x-y+3z+1=0 and at...

    Text Solution

    |

  5. Writing the equation of the plane 3x-2y+z+2=0 in normal form find its ...

    Text Solution

    |

  6. A variable plane moves in such a way that the sum of the reciprocals o...

    Text Solution

    |

  7. In each of the following case, verift whether the four given points ar...

    Text Solution

    |

  8. Find the points of intersection of the line (x-1)/1=(y+2)/ 3 =(z-1)/(...

    Text Solution

    |

  9. Find the angle between the plane x+y+4=0 and the line (x+3)/2=(y-1)/1=...

    Text Solution

    |

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

    Text Solution

    |

  11. Find the equation of the bisector planes of the angles between the pla...

    Text Solution

    |

  12. A variable plane meets the coordinate axes at P, Q, R points. If the p...

    Text Solution

    |

  13. Find the equation of the straight line perpendicular to the line (x-2)...

    Text Solution

    |

  14. Find the distance of the point (1,-2,3) from the plane x-y+z=5, measur...

    Text Solution

    |

  15. Prove that the lines frac[x+3][2]=frac[y+5][3]=frac[z-7][-3] and frac[...

    Text Solution

    |

  16. Find the equation of the image of the line (x - 1)/2 = (y + 2)=( z - 1...

    Text Solution

    |

  17. Find the shortest distance between the lines  (x-8)/(3) = (y+9)/(-16) ...

    Text Solution

    |

  18. Find the equation of the straight line perpendicular to the line (x-2)...

    Text Solution

    |

  19. Find the distance of the point (-1,-5,-10) from the point of intersect...

    Text Solution

    |

  20. Find the distance of the point (1,-1,-10) from the line (x-4)/1=(y+3)/...

    Text Solution

    |