Home
Class 12
MATHS
If e is the eccentricity of the ellipse ...

If `e` is the eccentricity of the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`, `(altb)` then

A

`b^(2)=a^(2)(1-e^(2))`

B

`a^(2)=b^(2)(1-e^(2))`

C

`a^(2)=b^(2)(e^(2)-1)`

D

` b^(2)=a^(2)(e^(2)-1)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|390 Videos

  • HYPERBOLA

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|162 Videos

Similar Questions

Explore conceptually related problems

The eccentricity of the ellipse (x^(2))/(36)+ (y^(2))/(16)=1 is

If e_(1) is the eccentricity of ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and e_(2) is the eccentricity of (x^(2))/(b^(2))+(y^(2))/(a^(2))=1 then

Find the eccentricity of the ellipse (x^2)/(9)+(y^2)/(4)=1

The eccentricity to the ellipse (x^(2))/(36)+(y^(2))/(16)=1 is

Find the eccentricity of the elipse ( x^(2))/( 16)+ ( y^(2) )/( 9) =1

The eccentricity of the ellipse 5 x^(2)+9 y^(2)=1 is

Find the eccentricity of the ellipse x^2/4+y^2/16=1

Find the area of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1

Find the eccentricity of the ellipse x^2/81+y^2/36=1

If e_(1) is the eccentricity of the ellipse (x^(2))/(16)+(y^(2))/(25)=1 and e_(2) is the eccentricity of the hyperbola passing through the foci of the ellipse and e_(1) . e_(2)=1 , then the equation of the hyperbola

HIMALAYA PUBLICATION-ELLIPSE-QUESTION BANK
  1. The equation of the ellipse whose focus is (1,-1) the directrix the li...

    Text Solution

    |

  2. The length of the latus rectum of the ellipse 3 x^(2)+4y^(2)=12 is

    Text Solution

    |

  3. If e is the eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)...

    Text Solution

    |

  4. The eccentricity of the ellipse 9x^(2) + 25y^(2) = 225 is

    Text Solution

    |

  5. The length of the latus rectum of the ellipse 49 x^(2)+64 y^(2)=3136

    Text Solution

    |

  6. The P is any point on the ellipse 4 x^(2)+16 y^(2)=64 whose foci are S...

    Text Solution

    |

  7. The product of the perpendiculars from the foci on any tangent to the ...

    Text Solution

    |

  8. Length of the latus rectum of the ellipse (x^(2))/(25)+(y^(2))/(9)=1 ...

    Text Solution

    |

  9. The equation of the ellipse whose one focus is at (4,0) and whose ecce...

    Text Solution

    |

  10. The centre of the ellipse 9 x^(2)+5 y^(2)-36 x-50 y+116=0 is

    Text Solution

    |

  11. If y=x+c is a tangent to the ellipse 9 x^(2)+16 y^(2)=144, thenc=

    Text Solution

    |

  12. If the latus-rectum of the ellipse is half the minor axis, then its ec...

    Text Solution

    |

  13. Eccentricity of the ellipse 25 x^(2)+9 y^(2)-150 x-90 y+225=0

    Text Solution

    |

  14. An ellipse with eccentricity e=(1)/(2) has a focus at (0,0) and the co...

    Text Solution

    |

  15. An ellipse has a minor axis of Iength 6 and the distance between its f...

    Text Solution

    |

  16. In an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 if the distance betwee...

    Text Solution

    |

  17. The angle between the lines joining the foci of an ellipse to an extre...

    Text Solution

    |

  18. The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 cuts the x -axis at A an...

    Text Solution

    |

  19. The locus of the point of intersection of two perpendicular tangents t...

    Text Solution

    |

  20. An ellipse has its centre (1,-1) and semi major axis is 8, which passe...

    Text Solution

    |