First slide

From a point A common tangents are drawn to the circle x2+y2=a22 and the parabola y2 = 4 ax. If the area of the quadrilateral formed by the common tangents, the chords of contact of the point A, w.r.t. the circle and the parabola  is λ square unit, then the value of 256a2λ  must be


Here, centre of the circle is the vertex of the parabola and both circle and parabola are symmetrical about axis of parabola . in this case the point of intersection of common tangent must lie on the directrix and axis of the parabola.

i.e, A-a,0

chord of contact of circle w,r,t   A-a,0 is



coordinates of R is -a2,a2 and  chord of contact of  parabola w.r.t A-a,0 is

y.0=2ax-a  i.e x=a

coordinates of P is (a,2a)

Area of quadrilateral PQRS' 

=2Area of PAS-Area of RAN




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