Home
Class 11
MATHS
If the area of the auxiliary circle of t...

If the area of the auxiliary circle of the ellipse `(x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1 (a gt b)` is twice the area of the ellipse, then the eccentricity of the ellipse is

A

`(1)/(sqrt2)`

B

`(sqrt3)/(2)`

C

`(1)/(sqrt3)`

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • CIRCLE AND CONICS

    TARGET PUBLICATION|Exercise COMPETITIVE THINKING|158 Videos

  • FACTORIZATION FORMULAE

    TARGET PUBLICATION|Exercise EVALUATION TEST|8 Videos

Similar Questions

Explore conceptually related problems

Equation auxiliary circle of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (a

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

Area of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is pi ab

The area enclosed by the : ellipse (x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1 is :

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

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

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

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

The intercept made by the auxiliary circle of the ellipse (x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1 (a gt b gt 1) on any tangent to the ellipse, subtends a right angle at its ceotre if

TARGET PUBLICATION-CIRCLE AND CONICS -EVALUATION TEST
  1. Tht line L passes through the points f intersection of the circles x ^...

    Text Solution

    |

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

    Text Solution

    |

  3. Let the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=...

    Text Solution

    |

  4. An ellipse drawn by taking a diameter of the circle (x-1)^(2)+y^(2)=1 ...

    Text Solution

    |

  5. The circle x^2 +y^2=4x+8y+ 5 intersects the line 3x-4y= m at two disti...

    Text Solution

    |

  6. Three distinct points A, B and C are given in the 2-dimensional coordi...

    Text Solution

    |

  7. The ellipse x^2+""4y^2=""4 is inscribed in a rectangle aligned with...

    Text Solution

    |

  8. The equation of the the circle having x - y - 2 = 0 and x - y + 2 = 0 ...

    Text Solution

    |

  9. The sum of the minimum distance and the maximum distnace from the poin...

    Text Solution

    |

  10. Let f(x,y) =0 be the equation of a circle. If f (0, lamda)=0 has equal...

    Text Solution

    |

  11. The distance between the vertex of the parabola y = x^2 - 4x + 3 and...

    Text Solution

    |

  12. Let a circle touches to the directrix of a parabola y ^(2) = 2ax has i...

    Text Solution

    |

  13. Through the vertex 'O' of parabola y^2=4x, chords OP and OQ are drawn...

    Text Solution

    |

  14. For each point (a,y) on an ellipse, the sum of the distances from (x,y...

    Text Solution

    |

  15. The line passing through the extremity A of the major exis and extremi...

    Text Solution

    |

  16. In an ellipse, if the lines joining focus to the extremities of the mi...

    Text Solution

    |

  17. If the area of the auxiliary circle of the ellipse (x ^(2))/(a ^(2)) +...

    Text Solution

    |

  18. If A and B are two fixed points and P is a variable point such that P...

    Text Solution

    |

  19. If A and B are two fixed points and P is a variable point such that P...

    Text Solution

    |

  20. If the line y = 7x - 25 meets the circle x^(2) + y^(2) = 25 in the poi...

    Text Solution

    |