Maths
General
Easy
Question
Tangents are drawn to the ellipse at the ends of the latus rectum. The are of the quadrilateral so formed is
 27


 45
Hint:
The eccentricity of an ellipse is always less than 1. i.e. e < 1. The eccentricity of an ellipse can be taken as the ratio of its distance from the focus and the distance from the directrix.
Eccentricity of ellipse (e) =
Here a is the length of the semimajor axis and b is the length of the semiminor axis.
The correct answer is: 27
Let LL′ and MM′ are the latus rectum.
Eccentricity of ellipse (e) =
Here a is the length of the semimajor axis and b is the length of the semiminor axis.
The equation of tangent at (x1,y1) is
The tangent passes through point L (ae,
,
So, the tangent cuts the xaxis at point A(a/e,0) and yaxis at point B(0,a)
Area of quadrilateral ABCD = 4×area of △OAB
Area of quadrilateral ABCD =
Area of quadrilateral ABCD =
Area of quadrilateral ABCD =
Area of quadrilateral ABCD = 27sq. units
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