Home
Class 12
MATHS
A variable plane moves in such a way tha...

A variable plane moves in such a way that the sum of the reciprocals of its intercepts on co-ordinate axes is constant. Show that the plane passes through a fixed point.

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

Show that the sum of the intercepts on the coordinate axes of any tangent to the curve sqrt x + sqrt y = sqrt a is constant.

Find the intercepts of a plane 3x+4y=7z=84 on co-ordinate axes.

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

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

Find the equation of the ellipse in each of the following cases: centre at (0,0) axes parallel to co-ordinate axes eccentricity is sqrt3/2 and the ellipse passing through the point (sqrt3,1/2).

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) .

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

    |