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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

A
3x2+4y2=48
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B
3x2+4y2=36
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C
4x2+3y2=36
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D
4x2+3y2=48
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Solution

## The correct option is A 3x2+4y2=48Since, 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=1−b2a2 b2a2=1−e2=34 Also, one directrix is x=8 ae=8⇒a=4 b2=3×4=12 Equation of ellipse becomes x216+y212=1 3x2+4y2=48

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