Home
Class 12
MATHS
An ellipse has O B as the semi-minor ...

An ellipse has `O B` as the semi-minor axis, `Fa n dF '` as its foci, and `/_F B F '` a right angle. Then, find the eccentricity of the ellipse.

A

`1/(sqrt(3))`

B

`1/4`

C

`1/2`

D

`1/(sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
Since, `anglefbf'=90^(@), then angleobc'=45^(@)andanglebf'0=45^(@) `
`rArr ae=b[since,Deltabof' is an isosceles triangle] and `e^(2)=1-b^(2)/(a2) `
`rArr e^(2)=1-(a^(2)e^(2))/(a^(2))`
`rArr e=1/sqrt2`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL DISTRIBUTION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|6 Videos

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|16 Videos

Similar Questions

Explore conceptually related problems

An ellipse has OB as the semi-minor axis,F and F' as its foci,and /_FBF' a right angle.Then,find the eccentricity of the ellipse.

B is extermity of the minor axis of an elipse whose foci are S and S'. If angle SBS' is a right angle, then the eccfentricity of the ellipse is

If OB is the semi-minor axis of an ellipse, F_1 and F_2 are its foci and the angle between F_1B and F_2B is a right angle, then the square of the eccentricity of the ellipse is

If the lines joining the foci of an ellipse to an end of its minor axis are at right angles , then the eccentricity of the ellipse is e =

Let S and s' be the foci of an ellipse and B be one end of its minor axis . If SBS' is a isosceles right angled triangle then the eccentricity of the ellipse is

If the length of the minor axis of an ellipse is equal to half of the distance between the foci then the eccentricity of the ellipse is

Pa n dQ are the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and B is an end of the minor axis. If P B Q is an equilateral triangle, then the eccentricity of the ellipse is 1/(sqrt(2)) (b) 1/3 (d) 1/2 (d) (sqrt(3))/2

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-CIRCLE AND CONICS-All Questions
  1. If the line y = 7x - 25 meets the circle x^(2) + y^(2) = 25 in the poi...

    Text Solution

    |

  2. The nearest point on the circle x^2 +y^2-6x + 4y-12=0 from (-5,4) is

    Text Solution

    |

  3. One of the diameters of the circle x^2+y^2-12x+4y+6=0 is given by

    Text Solution

    |

  4. A parabola has the origin as its focus and the line x""=""2 as the ...

    Text Solution

    |

  5. A focus of an ellipse is at the origin. The directrix is the line x =4...

    Text Solution

    |

  6. The directrix of the parabola y^(2)+4x+3=0is

    Text Solution

    |

  7. If the distance between the foci and the distance between the directri...

    Text Solution

    |

  8. The focal distance of a point on the parabola y^2= 16x whose ordinat...

    Text Solution

    |

  9. the equation of the circle passing through the foci of the ellip...

    Text Solution

    |

  10. If ea n de ' the eccentricities of a hyperbola and its conjugate, p...

    Text Solution

    |

  11. If the eccentricity of a hyperbola is sqrt(3), the eccentricity of its...

    Text Solution

    |

  12. If (-1,-2sqrt2)is one of exteremity of a focal chord of the parabola ...

    Text Solution

    |

  13. The latus rectum of a parabola whose focal chord is PSQ such that SP =...

    Text Solution

    |

  14. An ellipse has O B as the semi-minor axis, Fa n dF ' as its foci...

    Text Solution

    |

  15. Distance between foci is 8 and distance between directrices is 6 of hy...

    Text Solution

    |

  16. The eccenttricity of the hyperbola x^(2)/16-y^(2)/25=1is

    Text Solution

    |

  17. The eccentricity of the ellipse

    Text Solution

    |

  18. Find the locus of a point whiich moves in such a way that the sum of i...

    Text Solution

    |

  19. The cable of a uniformly loaded suspension bridge hangs in the form...

    Text Solution

    |

  20. An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high ...

    Text Solution

    |