Home
Class 11
MATHS
For the hyperbola (x^(2))/(cos^(2)alpha)...

For the hyperbola `(x^(2))/(cos^(2)alpha)-(y^(2))/(sin^(2)alpha)=1`, which of the following remains constant when `alpha` varies

A

Directrix

B

Abscissae of vertices

C

Abscissae of foci

D

Eccentricity.

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    MODERN PUBLICATION|Exercise EXERCISE|478 Videos
  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise EXERCISE|291 Videos
  • INFINITE SERIES

    MODERN PUBLICATION|Exercise EXAMPLE|10 Videos

Similar Questions

Explore conceptually related problems

For the hyperbola x^2/ cos^2 alpha - y^2 /sin^2 alpha = 1;(0 lt alphalt pi/4) . Which of the following remains constant when alpha varies?

For hyperbola x^2sec^2alpha-ycos e c^2alpha=1, which of the following remains constant with change in 'alpha'

Consider the ellipse x^(2)/(tan^(2)alpha)+y^(2)/(sec^(2)alpha)=1 where alphain(0,pi/2) . Which of the following quantities would vary as alpha varies?

Prove that the locus of the middle-points of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 which pass through a fixed point (alpha, beta) is a hyperbola whose centre is ((alpha)/(2), (beta)/(2)) .

Write the value of |[[cos alpha,-sin alpha],[sin alpha,cos alpha]] from the following :

Let alpha and beta be non-zero real numbers such that 2 ( cos beta - cos alpha) + cos alpha cos beta =1 . Then which of the following is/are true ?

The angle between the lines (x^(2)+y^(2))sin^(2)alpha=(x cos beta-y sin beta)^(2) is

Show that cos^(2)theta+cos^(2)(alpha+theta)-2cos alpha cos theta cos (alpha+beta) is independent of theta .

MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
  1. The equation of a tangent to the parabola y^2=""8x""i s""y""=""x""+"...

    Text Solution

    |

  2. A hyperbola having the transverse axis of length 2sintheta, is confoca...

    Text Solution

    |

  3. For the hyperbola (x^(2))/(cos^(2)alpha)-(y^(2))/(sin^(2)alpha)=1, whi...

    Text Solution

    |

  4. The perpendicular bisector of the line segment joining P(1,4) and Q (k...

    Text Solution

    |

  5. The point diametrically opposite to the point P(1,0) on the circle x^(...

    Text Solution

    |

  6. A parabola has the origin as its focus and the line x=2 as the directr...

    Text Solution

    |

  7. A focus of an ellipse Is that the rigin. The directrix is the line x=4...

    Text Solution

    |

  8. Consider three points : P (- sin (beta- alpha), - cos beta), Q = (cos...

    Text Solution

    |

  9. Consider two curves C1:y^2=4x ; C2=x^2+y^2-6x+1=0. Then,

    Text Solution

    |

  10. Let a and b be non-zero real numbers. Then the equation : (ax^2 + by^2...

    Text Solution

    |

  11. Consider a branch of the hyperbola : x^2 -2y^2-2sqrt2x-4sqrt2y-6=0 wit...

    Text Solution

    |

  12. Tangents drawn from the piont P(1,8) to the circle x^(2)+y^(2)-6x-4y-1...

    Text Solution

    |

  13. The tangent PT and the normal PN to the parabola y^2=4ax at a point P ...

    Text Solution

    |

  14. The line passing through the extremity A of the major axis and extremi...

    Text Solution

    |

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

    Text Solution

    |

  16. The normal at a point P, on the ellipse x^2+4y^2=16 meets the x-axis a...

    Text Solution

    |

  17. The locus of the orthocentre of the triangle formed by the lines : (1 ...

    Text Solution

    |

  18. An ellipse intersects the hyperbola 2x^2- 2y^2 = 1 orthogonally. The e...

    Text Solution

    |

  19. The lines p(p^(2)+1)x-y+q=0 and (p^(2)+1)^(2)x+(p^(2)+1)y+2q = 0 are ...

    Text Solution

    |

  20. If P and Q are the points of intersection of the circles x^(2)+y^(2)+3...

    Text Solution

    |