Home
Class 12
MATHS
An ellipse with the eccentricity e = 1/2...

An ellipse with the eccentricity e = 1/2 has a focus at (0, 0) and the corresponding directix is x+6=0. The equation of the ellipse is

A

`3x^(2)+4y^(2)+12x-36=0`

B

`3x^(2)+4y^(2)-12x+36=0`

C

`3x^(2)+4y^(2)-12x-36=0`

D

none

Text Solution

Verified by Experts

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ELLIPSE

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1B|24 Videos
  • ELLIPSE

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 SET - 1|2 Videos
  • ELLIPSE

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 SET - 2|1 Videos
  • EAMCET - 2016 TS

    DIPTI PUBLICATION ( AP EAMET)|Exercise Questions|80 Videos
  • EXPONENTIAL SERIES & LOGARITHMIC SERIES (APPENDIX-1)

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 SET - 4|5 Videos

Similar Questions

Explore conceptually related problems

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

An ellipse has eccentricity 1/2 and the focus at the point P(1/2,1) . Its one directrix is the common tangent, nearer to the point P, to the hyperola x^(2)-y^(2)=1 and the circle x^(2)+y^(2)=1 . Find the equation of the ellipse.

Knowledge Check

  • Focus (4, 0), e = 1/2 , directrix is x -16 = 0. Then equation of the ellipse is

    A
    `(x^(2))/(16)+(y^(2))/(9)=1`
    B
    `(x^(2))/(64)+(y^(2))/(32)=1`
    C
    `(x^(2))/(64)+(y^(2))/(48)=1`
    D
    `(x^(48))/(16)+(y^(2))/(64)=1`
  • For an ellipse with eccentricity 1/2 the centre is at the origin, if one directrix is x=4, then the equation of the ellipse is

    A
    `3x^(2)+4y^(2)=1`
    B
    `3x^(2)+4y^(2)=12`
    C
    `4x^(2)+34y^(2)=1`
    D
    `4x^(2)+3y^(2)=12`
  • A conic has latus rectum length 1, focus at (2,3) and the corresponding directrix is x+y -3=0 . Then the conic is

    A
    a parabola
    B
    an ellipse
    C
    a hyperbola
    D
    a rectangular hyperbola
  • Similar Questions

    Explore conceptually related problems

    (i) Find the equation of the ellipse whose focus (-1,1)’e = 1/2 and directrix is x - y + 3 = 0 (ii) Find the equation of the ellipse with focus at (l,-l),e = 2 //3 and directrix as x + y + 2 = 0 .

    For an ellipse with eccentricity (1)/(2) , the centre is at the origin. If one of its directrices is x=4 , then the equation of the ellipse is

    Foci are (0, pm 3), e = 3/4 , equation of the ellipse is

    Focus (3, 0), e = 3/5 , d irectrix 3x-25= 0, equation of the ellipse is

    The length of the latus rectum of an ellipse is 4. The focus and its corresponding directrix are (1, -2 ) and 3x + 4y - 15 = 0 then the eccentricity of the ellipse is