Home
Class 12
MATHS
The latus rectum LL^(') subtends a right...

The latus rectum `LL^(')` subtends a right angle at the centre of the ellipse, then its eccentricity is

A

`(sqrt(3)+1)/(2)`

B

`(sqrt(2)+1)/(2)`

C

`(sqrt(3)-sqrt(2))/(2)`

D

`(sqrt(5)-1)/(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 the latusrectum subtends a right angle at the centre of the hyperbola then its eccentricity

If the latus rectum through one focum subtends a right angle at the farther vertex of the hyperbola then its eccentricity is

If the latus rectum through one focus subtends a right angle at the farther vertex of the hyperbola then its eccntricity is

Statement-I : If a Iatusrectum of an ellipse subtends angle 60^(@) at the farthest vertex then eccentricity is 1-(1)/sqrt(3) Statement-II : If a Iatusrectum subtends 60^(@) at the centre of the ellipse then ecentricity is (sqrt(13)-1)/(2sqrt(3))

If the latus rectum of a hyperola forms an equilateral triangle with the centre of the hyperbola, then its eccentricity is

The tangent at a point P(acos theta,bsin theta) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets the auxillary circle in two points. The chord joining them subtends a right angle at the centre. Find the eccentricity of the ellipse:

If the latus rectum of a hyperbola forms an equilateral triangle with the vertex at the centre of the hyperbola , then its accentricity e=

A chord of a circle of radius 14 cm subtends a right angle at the centre. Find the areas of the minor and major segments of the circle.

A chord of a circle of radius 20 cm subtends a right angle at the centre find the corresponding minor segment.

AAKASH SERIES-ELLIPSE-PRACTICE EXERCISE
  1. The length of the latus rectum of an ellipse is 4. The focus and its c...

    Text Solution

    |

  2. Let P be a point on an ellipse whose parameter is (pi)/(3) . The sum a...

    Text Solution

    |

  3. The latus rectum LL^(') subtends a right angle at the centre of the el...

    Text Solution

    |

  4. If the latus rectum of a hyperola forms an equilateral triangle with t...

    Text Solution

    |

  5. Area of the quadrilateral formed by the extremities of major axis and ...

    Text Solution

    |

  6. If x+ky-5=0 is a tangent to the ellipse 4x^(2)+9y^(2)=20 then k =

    Text Solution

    |

  7. The equations of the tangents to the ellipse 3x^(2)+4y^(2)=12 which ar...

    Text Solution

    |

  8. The point of contact 4x-5y+25=0 with the ellipse 9x^(2)+25y^(2)=225 is

    Text Solution

    |

  9. The number of tangents to (x^(2))/(25)+(y^(2))/(9)=1 through (1,1) is

    Text Solution

    |

  10. The product of the slopes of the tangents to the ellipse 2x^(2)+3y^(2)...

    Text Solution

    |

  11. The radius of the director circle of 16x^(2)+9y^(2)=144 is

    Text Solution

    |

  12. The quadratic equation whose one root is (3+sqrt(5))/(2-sqrt(5)) is

    Text Solution

    |

  13. The equation to the auxiliary circle of (x^(2))/(12)+(y^(2))/(18)=1 is

    Text Solution

    |

  14. The equation of the normal to the ellipse x^(2)/4+y^(2)/1=1 at (2, -1)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |