Conics!

Algebra Level 4

From a point A A common tangents are drawn to the circle x2+y2=2 { x }^{ 2 }+{ y }^{ 2 }=2 and the parabola y2=8x { y }^{ 2 }=8x . Find the area of the quadrilateral formed by the common tangents, the chord of contact of the circle and the chord of contact of the parabola.

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