Home
Class 11
MATHS
If PQ is a double ordinate of the hyperb...

If PQ is a double ordinate of the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`
such that OPQ is an equilateral triangle, O being the centre of the hyperbola, then find range of the eccentricity (e) of the hyperbola.

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

If P Q is a double ordinate of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 such that O P Q is an equilateral triangle, O being the center of the hyperbola, then find the range of the eccentricity e of the hyperbola.

If PQ is a double ordinate of the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 such that Delta OPQ is equilateral, O being the centre. Then the eccentricity e satisfies

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

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

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 eccentricity of the hyperbola x^2-y^2=4 is

If the latus rectum of a hyperbola forms an equilateral triangle with the vertex at the center of the hyperbola ,then find the eccentricity of the hyperbola.

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

PQ is the double ordinate of the hyperbola x^2/a^2-y^2/b^2=1 and O is the centre of the hyperbola. If triangle OPQ is an equilateral triangle, then show that the eccentricity of this hyperbola is e) e^2 >4/3

If e is the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and theta is the angle between the asymptotes, then cos.(theta)/(2) is equal to

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. If the latus rectum of a hyperbola forms an equilateral triangle with ...

    Text Solution

    |

  2. If the rectum subtends a right angle at the centre of the hyperbola (x...

    Text Solution

    |

  3. If PQ is a double ordinate of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b...

    Text Solution

    |

  4. Find the equation of the hyperbola given by equations x=(e^t+e^(-t))/2...

    Text Solution

    |

  5. A ray emerging from the point (5, 0) is incident on the hyperbola 9x^2...

    Text Solution

    |

  6. Normal is drawn at one of the extremities of the latus rectum of the h...

    Text Solution

    |

  7. An ellipse and a hyperbola are confocal (have the same focus) and the ...

    Text Solution

    |

  8. The point of intersection of the tangents at the point P on the ellips...

    Text Solution

    |

  9. The distance between two directrices of a ractangular hyperbola is 10 ...

    Text Solution

    |

  10. Find the equation of normal to the hyperbola 3x^(2)-y^(2)=1 having slo...

    Text Solution

    |

  11. a triangle A B C with fixed base B C , the vertex A moves such that co...

    Text Solution

    |

  12. Find the equation of normal to the hyperbola x^(2)-9y^(2)=7 at point (...

    Text Solution

    |

  13. A circle has the same center as an ellipse and passes through the foci...

    Text Solution

    |

  14. The eccentricity of the conjugate hyperbola of the hyperbola x^2-3y^2=...

    Text Solution

    |

  15. P N is the ordinate of any point P on the hyperbola (x^2)/(a^2)-(y^2)/...

    Text Solution

    |

  16. Show that the equation 9x^2-16 y^2-18 x+32 y-151=0 represents a hyperb...

    Text Solution

    |

  17. Find the equation of hyperbola, whose center is (-3,2), one vertex is ...

    Text Solution

    |

  18. An ellipse passing through the origin has its foci (3, 4) and (6, 8). ...

    Text Solution

    |

  19. The locus of the point of intersection of the lines sqrt3 x- y-4sqrt3 ...

    Text Solution

    |

  20. Find the eccentricity of the hyperbola with asymptotes 3x+4y=2 and 4x-...

    Text Solution

    |