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AP EAMCET202018 Sep 2020Evening ShiftMathematicsEllipseActual

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

Options

  1. A(4 x^2+y^2=12 )
  2. B(x^2+3 y^2=12 )
  3. C(4 x^2+3 y^2=12 )
  4. D(3 x^2+4 y^2=12 )

Correct answer

D. (3 x^2+4 y^2=12 )

Step-by-step solution

Centre (=(0,0) ) Eccentricity (( e )= 1 2 ) Equation of directrix is (x=4 ) ( a e =4 ) ( a=4 e ) ( a=2 ) ( aligned b^2 & =a^2 (1-e^2 ) & =4 (1- 1 4 ) b^2 & =3 aligned ) ( ) Required Equation of Ellipse is ( x^2 4 + y^2 3 =1 ) (3 x^2+4 y^2=12 ) Hence, option (d) is correct.

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