Conics!

Algebra Level 5

From a point \( A \) common tangents are drawn to the circle \( { x }^{ 2 }+{ y }^{ 2 }=2 \) and the parabola \( { y }^{ 2 }=8x \). 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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