Home
Class 11
MATHS
If 0 lt alpha lt (pi)/(2), then which of...

If 0 `lt alpha lt (pi)/(2)`, then which of the following is independent of `alpha` in the case of the hyperbola `(x^(2))/(cos^(2)alpha) - (y^(2))/(sin^(2)alpha) = 1`?

A

eccentricity

B

coordinates of the vertex

C

equation of directrix

D

abscissa of the foci

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    CHHAYA PUBLICATION|Exercise VERY SHOT ANSWER TYPE QUESTIONS|16 Videos

  • HYPERBOLA

    CHHAYA PUBLICATION|Exercise VERY SHORT ANSWER TYPE QUESTIONS|1 Videos

  • HYPERBOLA

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITIVE EXAMS|12 Videos

  • DIAGRAMMATIC REPRESENTATION OF DATA

    CHHAYA PUBLICATION|Exercise EXERCISE (Very short Answer Type Question)|7 Videos

  • MATHEMATICAL INDUCTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams|20 Videos

Similar Questions

Explore conceptually related problems

If 0 lt alpha lt (pi)/(3) , then prove that alpha (sec alpha) lt (2pi)/(3).

If 0 lt alpha lt (pi)/(2) and sin alpha + cos alpha = sqrt2, then the value of cos 3 alpha is-

If 0 lt alpha lt pi/2 , then sqrt(2cotalpha+1/(sin^2alpha)) is equal to

If 0 lt alpha lt beta lt (pi)/(2) , prove that, tan alpha-tan beta lt alpha-beta .

show that (1-sin^2 alpha)(1-cos^2 alpha)(1+cot^2 alpha)(1+tan^2 alpha) = 1.

If (pi)/2 < alpha < (3pi)/2 then the modulus argument of (1+cos 2alpha)+i sin2alpha

Calculate the value of (sin^(6)alpha +cos^(6) alpha + 3sin^(2) alpha cos^(2) alpha).

The value of the integral int_(0)^(1)(dx)/(x^(2)+2x cos alpha +1),0ltalpha lt pi is

(sin alpha)/(sin 2x) +(cos alpha)/(cos 2x) =2

CHHAYA PUBLICATION-HYPERBOLA-MULTIPLE CHOICE TYPE QUESTIONS
  1. If e is the eccentricity of the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b...

    Text Solution

    |

  2. If 0 lt alpha lt (pi)/(2), then which of the following is independent ...

    Text Solution

    |

  3. If a point moves on a plane in such a way that the difference of its d...

    Text Solution

    |

  4. If e1 is the eccentricity of the hyperbola (y^(2))/(b^(2)) - (x^(2))/(...

    Text Solution

    |

  5. Eccentricity of a rectangular hyperbola is -

    Text Solution

    |

  6. The parametric equations of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(...

    Text Solution

    |

  7. The length of latus rectum of the hyperabola 9x^(2) - 25y^(2) = 225 is...

    Text Solution

    |

  8. The coordinates of foci of the hyperbola x^(2) - y^(2) = 4 are-

    Text Solution

    |

  9. The coordinates of the vertices of the hyperbola9x^(2)-16y^(2)=144 are...

    Text Solution

    |

  10. The length of the transverse axis of the hyperbola 9y^(2) - 4x^(2) = 3...

    Text Solution

    |

  11. In each of the find the coordinates of the foci and the vertices, the ...

    Text Solution

    |

  12. The length of latus rectum of the hyperabola 9y^(2) - 4x^(2) = 36 is -

    Text Solution

    |

  13. The length of the conjugate axis of the hyperbola 9x^(2) - 25y^(2) = 2...

    Text Solution

    |

  14. If foci of the ellipse (x^(2))/(16) + (y^(2))/(b^(2)) = 1 coincide wit...

    Text Solution

    |

  15. If e(1) and e(2) are the respective eccentricities of the hyperbola 4x...

    Text Solution

    |

  16. The eccentricity of the hyperbola 2x = a(t + (1)/(t)), 2y = a(t-(1)/(t...

    Text Solution

    |

  17. The distance between the two foci of the hyperbola x = 6 sec phi , y =...

    Text Solution

    |

  18. If e(1) and e(2) be the eccentricities of the hyperbolas 9x^(2) - 16y^...

    Text Solution

    |

  19. If the latus rectum of a hyperbola is equal to half of its transverse ...

    Text Solution

    |

  20. The difference of focal distances of any point on a hyperboal is equal...

    Text Solution

    |