Home
Class 12
MATHS
Find the eccentricity of the ellipse if ...

Find the eccentricity of the ellipse if
the length of rectum is equal to half the minor axis of the ellipse .

Text Solution

Verified by Experts

The correct Answer is:
`(sqrt(3))/(2)`
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    CHHAYA PUBLICATION|Exercise Short Answer Type Questios|48 Videos

  • ELLIPSE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams ( A M . C . Q )|5 Videos

  • ELLIPSE

    CHHAYA PUBLICATION|Exercise M . C . Q|20 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

  • GENERAL SOLUTIONS OF TRIGNOMETRIC EQUATIONS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type-|2 Videos

Similar Questions

Explore conceptually related problems

Find the eccentricity of the ellipse if the length of minor axis is equal to half the distance between the foci of the ellipse .

Show that the double ordinate of the auxiliary circle of an ellipse passing through the focus is equal to the minor axis of the ellipse .

What is the eccentricity of the ellipse whose length of minor axis is equal to the distance between the two foci?

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci , is

Taking the major and minor axes as the axes of coordinates, find the equation of the ellipse whose length of latus rectum is 8 and length of semi - major axis is 9

Taking the major and minor axes as the axes of coordinates, find the equation of the ellipse whose length of latus rectum is (32)/(5) . Unit and the coordinates of one focus are (3,0)

An ellipse and a hyperbola are confocal (have the same focus) and the conjugate axis of the hyperbola is equal to the minor axis of the ellipse. If e_1a n de_2 are the eccentricities of the ellipse and the hyperbola, respectively, then prove that 1/(e_1^2)+1/(e_2^2)=2 .

Taking major and minor axes as x and y - axes respectively , find the equation of the ellipse whose length of latus rectum is (18)/(5) unit and the coordinates of one focus are (4,0)

The latus rectum of an ellipse is equal to one-half of its minor axis. The eccentricity of the ellipse is

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the latus rectum of the ellipse (x^(2))/(25)+(y^(2))/(9)=1

CHHAYA PUBLICATION-ELLIPSE-Very Short Answer Type Qustions
  1. Find the equations of the directrices of the ellipse x^(2) + 4y^(2) =...

    Text Solution

    |

  2. Find the distance between the foci of the ellipse 3x^(2) + 4y^(2) = ...

    Text Solution

    |

  3. Find the eccentricity of the ellipse if the length of rectum is eq...

    Text Solution

    |

  4. Find the eccentricity of the ellipse if the length of minor axis ...

    Text Solution

    |

  5. Find the eccentricity of the ellipse if the length of minor axis i...

    Text Solution

    |

  6. If the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and (x^(2))/(p^(2...

    Text Solution

    |

  7. The ellipse (x^(2))/(169) + (y^(2))/(25) = 1 has the same eccentri...

    Text Solution

    |

  8. Find the positions of the points (i) (-3,1) (ii) (-2,-3) and (ii...

    Text Solution

    |

  9. For what values of a^(2) does the point (2sqrt(3), 1) lie outsid...

    Text Solution

    |

  10. The coordinates of the point on the ellipse 9x^(2) + 16y^(2) = 144 ...

    Text Solution

    |

  11. Find the coordinates of a point on the ellipse x^(2) + 2y^(2) = 4 ...

    Text Solution

    |

  12. If the ellipse (x^(2))/(a(1)^(2))+(y^(2))/(b(1)^(2))=1(a(1)^(2)gtb(1)^...

    Text Solution

    |

  13. Find (i) the centre, (ii) vertices, (iii) equations of the axes, (iv) ...

    Text Solution

    |

  14. Find (i) the centre, (ii) vertices, (iii) equations of the axes, (iv) ...

    Text Solution

    |

  15. Find (i) the centre, (ii) vertices, (iii) equations of the axes, (iv) ...

    Text Solution

    |

  16. Find the eccentricity, the length of latus rectum and the centre of e...

    Text Solution

    |

  17. Find the latus rectum , eccentricity and the coordinates of the foci o...

    Text Solution

    |

  18. Examine, with reasons, the validity of the following statement : x^(2...

    Text Solution

    |

  19. The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 passes through (-3 , ...

    Text Solution

    |

  20. The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 passes through the...

    Text Solution

    |