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Question

The eccentricity of an ellipse with it's centre at origin is 12. If one of the directrices is x=8, then the equation of the ellipse is given by
  1. 3x2+4y2=48
  2. 3x2+4y2=36
  3. 4x2+3y2=36
  4. 4x2+3y2=48


Solution

The correct option is A 3x2+4y2=48
Since, directrix is parallel to y-axis and center is origin, axis of ellipse is x-axis.
Let ellipse be represented by x2a2+y2b2=1, (a>b)
Then, e2=1b2a2
b2a2=1e2=34
Also, one directrix is x=8
ae=8a=4
b2=3×4=12
Equation of ellipse becomes
x216+y212=1
3x2+4y2=48

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