Home
Class 12
MATHS
Prove that the locus of mid points of th...

Prove that the locus of mid points of the chords `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` the tangents at the ends of which intersect on the circle `x^(2)+y^(2)=r^(2)` is `r^(2)((x^(2))/(a^(2))+(y^(2))/(b^(2)))^2=x^(2)+y^(2)`

Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    AAKASH SERIES|Exercise EXERCISE-I|52 Videos

  • ELLIPSE

    AAKASH SERIES|Exercise EXERCISE-II|68 Videos

  • ELLIPSE

    AAKASH SERIES|Exercise EXERCISE 4.3 (VERY SHORT ANSWER QUESTIONS)|4 Videos

  • DIFFERENTIAL EQUATIONS

    AAKASH SERIES|Exercise Practice Exercise|62 Videos

  • EXPONENTIAL SERIES

    AAKASH SERIES|Exercise EXERCISE - III|8 Videos

Similar Questions

Explore conceptually related problems

The locus of the mid points of the normal chords of ( x^(2) ) /(a^(2)) +(y^(2))/( b^(2)) = 1 is

The locus of mid points of the chords of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which pass through foot of a directrix

Prove that the points of intersection of two perpendicular tangents to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 lies on the circle x^(2)+y^(2)=a^(2)-b^(2)

If the locus of the mid points of the chords of the ellipse (x^(2))/(a^(2)) +(y^(2))/( b^(2)) =1 , drawn parallel to y=m_1x is y=m_2x then m_1m_2=

Find the locus of the mid-point of the chord of the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 which subtends a right angle at the origin.

The locus of poles with respect to the hyperbola x^(2)//a^(2) -y^(2)//b^(2) = 1 of tangents to its auxiliary circle is

Prove that the locus of the mid -points of the chords of the circle x^(2)+y^(2)=16 which are tangents to the hyperbola 9x^(2)-16y^(2)=144 is (x^(2)+y^(2))^(2)=16x^(2)-9y^(2) .

AAKASH SERIES-ELLIPSE-ADDITIONAL EXERCISE
  1. The tangent at a point P(theta) to the ellipse x^2/a^2+y^2/b^2=1 cuts ...

    Text Solution

    |

  2. If foci and the ends of the minor axis of an ellipse are the vertices ...

    Text Solution

    |

  3. Prove that the locus of an end of latusrectum of all ellipses having a...

    Text Solution

    |

  4. Show that the length of common tangent to the ellipse 'x^(2)/(25)+y^(2...

    Text Solution

    |

  5. Let d be the perpendicular distance from the centre of the ellipse x^(...

    Text Solution

    |

  6. Find the point on the curve 4x^(2) + a^(2)y^(2) = 4a^(2), 4lta^(2)lt8,...

    Text Solution

    |

  7. Prove that in an ellipse the perpendicular from focus upon any tangent...

    Text Solution

    |

  8. Let P be a point on the ellipse Let the line parallel to y-axis passin...

    Text Solution

    |

  9. Let P be a point on the ellipse Let the line parallel to y-axis passin...

    Text Solution

    |

  10. Consider the family of circles If in the 1st quadrant, the common tang...

    Text Solution

    |

  11. Show that the maximum distance of centre of the ellipse x^(2)/a^(2)+y^...

    Text Solution

    |

  12. The product of the perpendiculars from the foci on any tangent to the...

    Text Solution

    |

  13. Prove that the locus of mid points of the chords (x^(2))/(a^(2))+(y^(2...

    Text Solution

    |

  14. Prove that the locus of mid points of the chords (x^(2))/(a^(2))+(y^(2...

    Text Solution

    |

  15. Find the shortest distance between the ellipse x^(2) + 2y^(2) = 2 and ...

    Text Solution

    |

  16. Given the base of the triangle and the sum of tangent of base angles a...

    Text Solution

    |

  17. If a circle intercepts the ellipse at four points, show that the sum o...

    Text Solution

    |

  18. If a line is drawn through a point A(3,4) to cut the circle x^(2)+y^(2...

    Text Solution

    |

  19. From a variable point P tangents are drawn to the ellipse 4x^(2) + 9y^...

    Text Solution

    |

  20. Tangents are drawn to the ellipse (x^(2))/(a^(2)) +(y^(2))/( b^(2)) =a...

    Text Solution

    |