Home
Class 12
MATHS
If ea n de ' the eccentricities of a hyp...

If `ea n de '` the eccentricities of a hyperbola and its conjugate, prove that `1/(e^2)+1/(e '^2)=1.`

A

`-1`

B

0

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
c
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    MCGROW HILL PUBLICATION|Exercise EXERCISE LEVEL 2 (SINGLE CORRECT ANSWER TYPE QUESTIONS)|18 Videos

  • HYPERBOLA

    MCGROW HILL PUBLICATION|Exercise QUESTION FROM PREVIOUS YEARS AIEEE/JEE MAIN PAPERS|23 Videos

  • HYPERBOLA

    MCGROW HILL PUBLICATION|Exercise EXERCISE (CONCEPT -BASED SINGLE CORRECT ANSWER TYPE QUESTIONS)|15 Videos

  • HEIGHTS AND DISTANCES

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|3 Videos

  • INDEFINITE INTEGRATION

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B - ARCHITECTURE ENTRANCE EXAMINATION PAPERS|11 Videos

Similar Questions

Explore conceptually related problems

If e and e' the eccentricities of a hyperbola and its conjugate,prove that (1)/(e^(2))+(1)/(e^(2))=1

If e_1 and e_2 be the eccentricities of hyperbola and its conjugate, then 1/e^2_1 + 1/e^2_2 = (A) sqrt(2)/8 (B) 1/4 (C) 1 (D) 4

Let e_1 and e_2 be the eccentricities of a hyperbola and its conjugate hyperbola respectively. Statement 1 : e_1 e_2 gt sqrt(2) . Statement 2 : 1/e^2_1 + 1/e^2_2 =

If e_(1) and e_(2) are the eccentricities of the hyperbola and its conjugate hyperbola respectively then (1)/(e_(1)^(2))+(1)/(e_(2)^(2)) is equal to

If e_(1) and e_(2) are the eccentricities of a hyperbola 3x^(2)-2y^(2)=25 and its conjugate, then

If a variable line has its intercepts on the coordinate axes e and e', where (e)/(2) and (e')/(2) are the eccentricities of a hyperbola and its conjugate hyperbola,then the line always touches the circle x^(2)+y^(2)=r^(2), where r=1 (b) 2 (c) 3 (d) cannot be decided

If e and e\' are the eccentricities of the hyperbola x^2/a^2 - y^2/b^2 = 1 and its conjugate hyperbola, prove that 1/e^2 + 1+e\'^2 = 1

MCGROW HILL PUBLICATION-HYPERBOLA-EXERCISE LEVEL 1(SINGLE CORRECT ANSWER TYPE QUESTIONS)
  1. The curve described parametrically by x=t^2+t+1 , and y=t^2-t+1 repres...

    Text Solution

    |

  2. The point (at^2,2bt) lies on the hyperbola x^2/a^2-y^2/b ^2= 1 for

    Text Solution

    |

  3. If the coordinates of four concyclic point on the rec­tangular hyperbo...

    Text Solution

    |

  4. The eccentricity of a rectangular hyperbola, is

    Text Solution

    |

  5. If ea n de ' the eccentricities of a hyperbola and its conjugate, p...

    Text Solution

    |

  6. Foci of the rectangular hyperbola are (pm 7) the equation of the hype...

    Text Solution

    |

  7. The is a point P on the hyperbola (x^(2))/(16)-(y^(2))/(6)=1 such that...

    Text Solution

    |

  8. The normal at a point P to the parabola y^(2) = 4x is parallel to the ...

    Text Solution

    |

  9. The difference between the length 2a of the trans­verse axis of a hype...

    Text Solution

    |

  10. The locus of the point of intersection of the tangents to the hyperbol...

    Text Solution

    |

  11. If the asymptotes of the hyperbola perpendicular to the asymptotes of...

    Text Solution

    |

  12. P and Q are two points on the rectangular hyperbola xy = C^(2) such th...

    Text Solution

    |

  13. Normal at (3, 4) to the rectangular hyperbola x y - y - 2 x - 2 = 0 me...

    Text Solution

    |

  14. Find the locus of the-mid points of the chords of the circle x^2 + y^2...

    Text Solution

    |

  15. If the eccentricity of the hyperbola is sqrt(5) and the distance betwe...

    Text Solution

    |

  16. If the extremities of the latus rectum of the hyperbola with positive...

    Text Solution

    |

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

    Text Solution

    |

  18. The angle between the asymptotes of the hyperbola (x^(2))/(16)-(y^(2))...

    Text Solution

    |

  19. The parametric equation x=a(sec theta+tan theta),y=b(sec theta-tan t...

    Text Solution

    |

  20. If a normal to the hyperbola x^(2) - 4y^(2) = 4 having equal positive ...

    Text Solution

    |