Home
Class 12
MATHS
Find the eccentricity of an ellipse (x^(...

Find the eccentricity of an ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` whose latus reactum is half of its major axis.

A

`1sqrt(2)`

B

`sqrt(2//3)`

C

`sqrt(3)//2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • ELLIPSE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|7 Videos

  • DIFFERENTIATION

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • EXPONENTIAL AND LOGARITHMIC SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|20 Videos

Similar Questions

Explore conceptually related problems

Find the eccentricity of an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 whose latus rectum is half of its major axis.

the eccentricity of an ellipse (x^(2))/(a^(2))+(y^(2))=1 whose latus rectum is half of its minor axes , is

If the eccentricity of the ellipse, x^2/(a^2+1)+y^2/(a^2+2)=1 is 1/sqrt6 then latus rectum of ellipse is

Find the eccentricity of the ellipse (i) whose latus rectum is equal to half of its minor axis (ii) whose latus rectum is equal to half of its major axis (iii) if the major axis is three times the minor axis

If the length of the major axis intercepted between the tangent and normal at a point P (a cos theta, b sin theta) on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 is equal to the length of semi-major axis, then eccentricity of the ellipse is

Find the eccentricity of the ellipse whose latus rectum is (i) half its major axis, (ii) half its minor axis.

If eccentricity of the ellipse (x^(2))/(a^(2)+1)+(y^(2))/(a^(2)+2)=1 is (1)/(sqrt6) , then the ratio of the length of the latus rectum to the length of the major axis is

Find the equation of the normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at the positive end of the latus rectum.

If the normal at one end of the latus rectum of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 passes through one end of the minor axis, then prove that eccentricity is constant.

If the normal at one end of the latus rectum of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 passes through one end of the monor axis, then prove that eccentricity is constant.

OBJECTIVE RD SHARMA ENGLISH-ELLIPSE-Exercise
  1. If A and B are two fixed points and P is a variable point such that P...

    Text Solution

    |

  2. the length of the latusrectum of the ellipse 3x^(2) + y^(2) = 12 ....

    Text Solution

    |

  3. Find the eccentricity of an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 ...

    Text Solution

    |

  4. the eccentricity of an ellipse (x^(2))/(a^(2))+(y^(2))=1 whose l...

    Text Solution

    |

  5. If the focal distance of an end of the minor axis of an ellipse (ref...

    Text Solution

    |

  6. if 2y = x and 3y + 4x=0 are the equations of a pair of conjuga...

    Text Solution

    |

  7. if theta is a parameter then x=a ( sin theta + cos theta), y...

    Text Solution

    |

  8. The distance from the foci of P (x(1), y(1)) on the ellipse x^2/9+y^2/...

    Text Solution

    |

  9. Find the equation for the ellipse that satisfies the given conditions...

    Text Solution

    |

  10. The eccentricity of the curve x^(2)-4x+4y^(2)=12 is

    Text Solution

    |

  11. The parametric representation of a point on the ellipse whose foci are...

    Text Solution

    |

  12. if S and S are two foci of an ellipse (x^(2))/(a^(2))+(y^(2))/(b^...

    Text Solution

    |

  13. The eccentricity of the ellipse represented by 25 x^2+16 y^2-150 x-175...

    Text Solution

    |

  14. the length of the latusrectum of the ellipse 5x^(2) + 9x^(2)=45...

    Text Solution

    |

  15. The equation of the passing through the of the ellipse (x^(2))/(16)+(y...

    Text Solution

    |

  16. the eccentricity to the conic 4x^(2) +16y^(2)-24x-32y=1 is

    Text Solution

    |

  17. A set of points is such that each point is three times as far away fro...

    Text Solution

    |

  18. the foci of an ellipse are (0+-6) and the equation of the direc...

    Text Solution

    |

  19. An ellipse has its centre at (1,-1) and semi major axis =8 and it pass...

    Text Solution

    |

  20. Let L L ' be the latusrectum and S be a focus of the ellipse (x^...

    Text Solution

    |