Home
Class 12
MATHS
If alpha and beta are the eccentric angl...

If `alpha` and `beta` are the eccentric angles of the ends of a focal chord of the ellipse then `cos^(2)((alpha+beta)/(2))sec^(2)((alpha-beta)/(2))`=

A

`(a^(2)+b^(2))/(a^(2))`

B

`(a^(2)-b^(2))/(a^(2))`

C

`(a^(2))/(a^(2)+b^(2))`

D

`(a^(2))/(a^(2)-b^(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    AAKASH SERIES|Exercise EXERCISE-II|68 Videos
  • DIFFERENTIAL EQUATIONS

    AAKASH SERIES|Exercise Practice Exercise|62 Videos
  • EXPONENTIAL SERIES

    AAKASH SERIES|Exercise EXERCISE - III|8 Videos

Similar Questions

Explore conceptually related problems

If α, β are the eccentric angles of the extremeties of a focal chord of the ellipse (i) e cos (alpha+beta)/(2)=cos (alpha-beta)/(2) (ii) tan (alpha/2)tan (beta/2)=(e-1)/(e+1)

IF alpha,beta are the eccentric angles of the extremities of a focal chord of the ellipse x^2/a^2+y^2/b^2=1 . Then show that e cos""(alpha+beta)/2=cos""(alpha-beta)/2

If 3 sin alpha=5sin beta then (tan((alpha+beta)/2))/(tan((alpha-beta)/2))=

cos^(2)(alpha+beta)+cos^(2)(alpha-beta)-cos2alpha cos2beta=

(alpha + beta)^(2) - 2 alpha beta =

If alpha,beta are the ends of a focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then its eccentricity e is

The expression cos^(2)(alpha+beta)+cos^(2)(alpha-beta)-cos2alpha cos2beta , is

If cos alpha=3/5 and cos beta = 5/13 and alpha , beta are acute angles , then prove that cos^(2)((alpha+beta)/2)=16/65

If alpha , beta are supplementary angles , then cos^(2)alpha + sin^(2) beta =

AAKASH SERIES-ELLIPSE-PRACTICE EXERCISE
  1. The equation of the normal to the ellipse x^(2)/4+y^(2)/1=1 at (2, -1)...

    Text Solution

    |

  2. The equations of the tangents drawn from (2, 3) to the ellipse 9x^(2) ...

    Text Solution

    |

  3. If a gt b and e is the eccentricity of the ellipse then the equation ...

    Text Solution

    |

  4. If the normal at one end of latusrectum of an ellipse (x^(2))/(a^(2))...

    Text Solution

    |

  5. The equation to the locus of point of intersection of lines y-mx=sqr...

    Text Solution

    |

  6. The number of tangents that can be drawn to an ellipse perpendicular t...

    Text Solution

    |

  7. If the chords of contact of tangents from two points to the ellipse ar...

    Text Solution

    |

  8. The mid point of the chord 3x - 2y + 8 = 0 of the ellipse 3x^(2) + 4y^...

    Text Solution

    |

  9. The distance of a point on the ellipse x^(2) + 3y^(2) = 6 from its cen...

    Text Solution

    |

  10. The equation of the tangent at a point theta=3pi//4 to the ellipse x^(...

    Text Solution

    |

  11. The equation of the normal to the ellipse at the point whose eccentri...

    Text Solution

    |

  12. P is a point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 S and S...

    Text Solution

    |

  13. If the chord joining two points whose eccentric angles are alpha and ...

    Text Solution

    |

  14. If alpha and beta are the eccentric angles of the ends of a focal chor...

    Text Solution

    |

  15. The minimum area of triangle formed by the tangent to the ellipse (x^(...

    Text Solution

    |

  16. If a tangent to the ellipse meets major and minor axis at M and N resp...

    Text Solution

    |

  17. The locus of the variable point P for which the chord of contact of to...

    Text Solution

    |

  18. If pi+theta is the eccentric angle of a point on the ellipse 16x^(2)+2...

    Text Solution

    |

  19. The locus of midpoints of chords of the ellipse x^(2)//a^(2)+y^(2)//b^...

    Text Solution

    |

  20. If y = mx + c is a normal to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2...

    Text Solution

    |