Home
Class 11
MATHS
A bar of given length moves with its ext...

A bar of given length moves with its extremities on two fixed straight lines at right angles. Show that any point on the bar describes an ellipse.

Text Solution

AI Generated Solution

To show that any point on a bar of given length, moving with its extremities on two fixed straight lines at right angles, describes an ellipse, we can follow these steps: ### Step-by-Step Solution: 1. **Define the Setup**: - Let the two fixed lines be the x-axis (OX) and the y-axis (OY). - Let the length of the bar be \( L \). - Let the endpoints of the bar be \( A \) and \( B \). ...
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|236 Videos
  • FUNCTIONS

    RD SHARMA|Exercise Solved Examples And Exercises|157 Videos

Similar Questions

Explore conceptually related problems

If a bar of givenlength moves with its extremities on two fixed straight lines at right angles,then the locus of any point on bar marked on the bar describes a/an :

A bar of length 20 units moves with its ends on two fixed straight lines at right angles.A point P marked on the bar ata distance of 8 units from one end describes a conic whose eccentricity is

A straight rod of given length slides between two fixed bars which include an ingle of 90^(@) . Show that the locus of a point on the rod which divides it in a given ratio is an ellipse.If this ratio be 1/2, show that the eccentricity of the ellipse is sqrt(2)/3

A line of fixed length a+b moves so that its ends are always on two fixed perpendicular straight lines.Then the locus of the point which divides this line into portions of length a and bis a/an ellipse (b) parabola straight line (d) none of these

A straight line has its extremities on two fixed straight lines and cuts off from them a triangle of constant area c^(2). Then the locus of the middle point of the line is 2xy=c^(2)(b)xy+c^(2)=04x^(2)y^(2)=c(d) none of these

The locus of a point which moves difference of its distance from two fixed straight which are at right angles is equal to the distance from another fixed straight line is

If one of the four angles formed by two intersecting lines is a right angle,then show that each of the four angles is a right angle.

A point moves so that the sum of the squares of its distances from two intersecting straight lines is constant.Prove that its locus is an ellipse.

RD SHARMA-ELLIPSE-Solved Examples And Exercises
  1. A rod A B of length 15c m rests in between two coordinate axes in such...

    Text Solution

    |

  2. Find the equation of the ellipse whose foci are (2,3),(-2,3) and whose...

    Text Solution

    |

  3. A bar of given length moves with its extremities on two fixed strai...

    Text Solution

    |

  4. An arc is in the form of a semi-ellipse. It is 8m wide and 2m high a...

    Text Solution

    |

  5. Find the equation of the ellipse whose axes are along the coordinate a...

    Text Solution

    |

  6. Find the equation of the ellipse whose axes are along the coordinate ...

    Text Solution

    |

  7. Find the equation of the ellipse (referred to its axes as the axes o...

    Text Solution

    |

  8. A man running a racecourse notes that the sum of the distances from...

    Text Solution

    |

  9. Find the equation of the ellipse whose focus is (1,-2) the directrix 3...

    Text Solution

    |

  10. Find the equation of the ellipse in the following case: focus is (0,1)...

    Text Solution

    |

  11. Find the equation of the ellipse in the following case: focus is (-1,1...

    Text Solution

    |

  12. Find the equation of the ellipse in the following case: focus is (-2,3...

    Text Solution

    |

  13. Find the equation of the ellipse in the following case: focus is (1,2)...

    Text Solution

    |

  14. Find the eccentricity ,coordinates of foci ,length of the latus rectum...

    Text Solution

    |

  15. Find the eccentricity ,coordinates of foci, length of the latus rectum...

    Text Solution

    |

  16. Find the eccentricity ,coordinates of foci, length of the latus rectum...

    Text Solution

    |

  17. Find the eccentricity coordinates of foci, length of the latus rectum ...

    Text Solution

    |

  18. Find the eccentricity, coordinates of foci, length of the latus rectum...

    Text Solution

    |

  19. Find the equation to the ellipse (referred to its axes as the axes of ...

    Text Solution

    |

  20. Find the equation of the ellipse (referred to its axes as the axes o...

    Text Solution

    |