A trapezium is formed by the pair of tangents of parabola P : y = x 2 4 + 1 drawn from the centre of the ellipse E : x 2 4 + y 2 = 1 4 , tangent at the vertex of P and the tangent at end point of the minor axis of E . The area (in sq. units) of the trapezium is

Step-by-step solution

The equation of the tangents from the centre of the ellipse to the parabola are y = ± x The equation of the tangent at the vertex P of the parabola is y = 1 The equation of the tangent at the end point of the minor axis of the ellipse is y = 1 2 Hence, the area of trapezium A B C D = 1 2 ⋅ 1 2 1 + 2 = 3 4 sq. units