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The coordinates of any point, in the parametric form, on the ellipse whose foci are (-2,0),(8,0) and eccentricity 1 2 , is

Options

  1. A(5 2 , 5 )
  2. B(3+5 2 , 5 )
  3. C(3+5 , 5 2 )
  4. D(5 , 3+5 2 )

Correct answer

B. (3+5 2 , 5 )

Step-by-step solution

The foci are (-2,0) and (8,0) . The distance between the foci is 2 a e=10 array ll a e=5 e= 1 2 (given) a=5 2 Now , b^2=a^2 (1-e^2 ) b^2=50 (1- 1 2 )=25 b=5 array The centre of the ellipse is the mid-point of the line joining two foci. Therefore, the coordinates of the centre is (3,0) . Thus, the parametric coordinates of a point on Eq. (i) are (3+5 2 , 5 ) .

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