Home
Class 11
MATHS
Show that midpoint of focal chords of a ...

Show that midpoint of focal chords of a hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=i` lie on another hyperbola having same eccentricity.

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

Show that the midpoints of focal chords of a hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 lie on another similar hyperbola.

The parametric equations of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1 are-

the eccentricity of the hyperbola (x^(2))/(16)-(y^(2))/(25)=1 is

If e is the eccentricity of the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 , then e =

If the chords of contact of tangents from two points (-4,2) and (2,1) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are at right angle, then find then find the eccentricity of the hyperbola.

Let PQ be a double ordinate of the hyperboal (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1 .If O be the centre of the hyperbola and OPQ is an equilateral triangle, then prove that the eccentricity e gt 2/sqrt(3) .

The equation of the auxiliary circle of the hyperbola x^2/a^2-y^2/b^2=1 is

If the angle between the asymptotes of hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is (pi)/(3) , then the eccentricity of conjugate hyperbola is _________.

If e_1 is the eccentricity of the hyperbola (y^(2))/(b^(2)) - (x^(2))/(a^(2)) = 1 then e_(1) =

Show that for all values of t the point x=c((1+t^2)/(1-t^2)) , y=(2ct)/(1-t^2) lia.on a on a fixed hyperbola. What is the eccentricity of the hyperbola.

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. The locus of a point, from where the tangents to the rectangular hyp...

    Text Solution

    |

  2. The tangent at a point P on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(...

    Text Solution

    |

  3. Show that midpoint of focal chords of a hyperbola (x^(2))/(a^(2))-(y^(...

    Text Solution

    |

  4. The curve for which the length of the normal is equal to the length ...

    Text Solution

    |

  5. A tangent drawn to hyperbola x^2/a^2-y^2/b^2 = 1 at P(pi/6) froms a t...

    Text Solution

    |

  6. The equation of the transvers axis of the hyperbola (x-3)^2+(y+1)^2=(4...

    Text Solution

    |

  7. If a variable line has its intercepts on the coordinate axes e and e^(...

    Text Solution

    |

  8. The locus of the point which is such that the chord of contact of ta...

    Text Solution

    |

  9. The angle between the lines joining the origin to the points of inters...

    Text Solution

    |

  10. The equation of the chord joining two points (x(1),y(1)) and (x(2),y(2...

    Text Solution

    |

  11. If P(x1,y1),Q(x2,y2),R(x3,y3) and S(x4,y4) are four concyclic points...

    Text Solution

    |

  12. Suppose the circle having equation x^(2)+y^(2)=3 intersects the rectan...

    Text Solution

    |

  13. Let two points P and Q lie on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b...

    Text Solution

    |

  14. Let C be a curve which is the locus of the point of intersection of li...

    Text Solution

    |

  15. The ellipse 4x^2+9y^2=36 and the hyperbola a^2x^2-y^2=4 intersect at r...

    Text Solution

    |

  16. The chord P Q of the rectangular hyperbola x y=a^2 meets the axis of x...

    Text Solution

    |

  17. The curve xy = C, (c gt 0), and the circle x^(2)+y^(2)=1 touch at two ...

    Text Solution

    |

  18. If S(1) and S(2) are the foci of the hyperbola whose length of the tra...

    Text Solution

    |

  19. The locus of the point which is such that the chord of contact of ta...

    Text Solution

    |

  20. The asymptote of the hyperbola x^2/a^2-y^2/b^2=1 form with an tangent ...

    Text Solution

    |