Home
Class 11
MATHS
The eccentricity of an ellipse, with its...

The eccentricity of an ellipse, with its centre the origin, is `1/2`. If one of the directrices is x = 4, the equation of the ellipse is :

A

`3x^2+4y^2=1`

B

`3x^2+4y^2=12`

C

`4x^2+3y^2=12`

D

`4x^2+3y^2=1` .

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    MODERN PUBLICATION|Exercise EXERCISE|478 Videos

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise EXERCISE|291 Videos

  • INFINITE SERIES

    MODERN PUBLICATION|Exercise EXAMPLE|10 Videos

Similar Questions

Explore conceptually related problems

The eccentricity of an ellipse whose centre is at the origin is 1/2 . If one of its directrices is x = - 4, then the equation of the normal to it at (1, 3/2) is :

The eccentricity of the ellipse 4x^2 + 9y^2 = 36 is :

An ellipse is drawn by taking a diameter of the circle (x-1)^2+y^2=1 as its semi-minor axis and a diameter of the circle x^2+(y-2)^2=4 as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is (1) 4x^2+""y^2=""4 (2) x^2+""4y^2=""8 (3) 4x^2+""y^2=""8 (4) x^2+""4y^2=""16

If the eccentricity of an ellipse is 1/sqrt2 , then its latusrectum is equal to its

Find the eccentricity of the ellipse if : the latus-rectum is one half of its minor axis.

The eccentricity of the ellipse : x^2+4y^2+8y-2x+1=0 is :

The distance between the directrices of the ellipse x^2/4+y^2/9=1 is:

Find the eccentricity of the ellipse if : the latus-rectum is one half of its major axis.

The eccentricity of the ellipse x^2/a^2+y^2/b^2=1 , if its latus rectum is half of its minor axis, is :

The ellipse x^2+ 4y^2 = 4 is inscribed is a rectangle alligned with the co-ordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is :

MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
  1. Which one of the following is independent of alpha in the hyperbola (0...

    Text Solution

    |

  2. Angle between tangents drawn from the point (1, 4) to the parabola y^2...

    Text Solution

    |

  3. The eccentricity of an ellipse, with its centre the origin, is 1/2. If...

    Text Solution

    |

  4. If the line 2x+sqrt(6)y=2 touches the hyperbola x^(2)-2y^(2)=4, then t...

    Text Solution

    |

  5. The line parallel to the x-axis and passing through the intersection o...

    Text Solution

    |

  6. If non-zero numbers a,b,c are in H.P., then the straight line x/a+ y/b...

    Text Solution

    |

  7. If a vertex of a triangle is (1, 1) and the mid-points of two side thr...

    Text Solution

    |

  8. If the circles : x^2+ y^2+2ax + cy +a=0 and x^2+ y^2-3ax+dy -1=0 inter...

    Text Solution

    |

  9. A circle touches the X-axis and also touches the centre at (0,3) and r...

    Text Solution

    |

  10. If a circle passes through the point (a, b) and cuts the circle x^2+ y...

    Text Solution

    |

  11. An ellipse has OB as semi minor axis, F and F' its focii eccentricity ...

    Text Solution

    |

  12. The locus of a point P(alpha, beta) moving under the condition that th...

    Text Solution

    |

  13. A circle is given by x^2 + (y-1)^2 = 1, another circle C touches it ex...

    Text Solution

    |

  14. The minimum area of the triangle formed by the tangent to (x^2)/(a^2)+...

    Text Solution

    |

  15. A straight line through the point A(3,4) is such that its intercept be...

    Text Solution

    |

  16. If (a,a^(2)) falls inside the angle made by the lines y = x/2 , x gt ...

    Text Solution

    |

  17. If the lines 3x - 4y- 7 = 0 and 2x - 3y- 5 = 0 are two diameters of a ...

    Text Solution

    |

  18. Let C be the circle with centre (0, 0) and radius 3 units. The equatio...

    Text Solution

    |

  19. The locus of the vertices of the family of parabolas y=(a^3x^2)/3+(a^2...

    Text Solution

    |

  20. Angle between the tangents to the curve y=x^2-5x+6 at the points (2,0)...

    Text Solution

    |