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AP EAMCET2008MathematicsEllipse

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

Options

  1. A3 x^2+4 y^2=1
  2. B3 x^2+4 y^2=12
  3. C4 x^2+3 y^2=1
  4. D4 x^2+3 y^2=12

Correct answer

B. 3 x^2+4 y^2=12

Step-by-step solution

Given that, e= 1 2 and a e =4 array lrl & a 1 / 2 =4 a=2 Using & b^2=a^2 (1-e^2 ) & b^2=4 (1- 1 4 )=3 array Equation of ellipse is aligned x^2 4 + y^2 3 & =1 3 x^2+4 y^2 & =12 aligned

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