A Tangent, Two Perpendiculars and a Trapezoid

Difficulty: Medium · Topics: Geometry, Conic Sections, Parabola

Urinma, ikki perpendikulyar va trapetsiya

Let P be a point in the first quadrant on the parabola y^2=4x, let l be the tangent line to the parabola at P, and let Q be the point where l meets the y-axis.

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The lines perpendicular to l through P and through Q meet the x-axis at the points S and R respectively, and overlineRS=10.

Find the area of the quadrilateral PQRS.