Answer:
Option D
Explanation:
Plan
(i) y=mx+\frac{a}{m} is equation of tangent to the parabola y2=4ax
(ii) A line is atangent to circle , if distance of line from centre is equal to the radius of circle.
(iii) Equation of chord drawn from exterior point (x1,y1) to a circle/parabola is given by T=0
(iv) Area of Trapezium= 1/2 ( sum of parallel sides) x ( distance between them)
Let equation of tangent to parabola be
y=mx+\frac{2}{m}
It also touches the circle x2+y2=2
\therefore |\frac{2}{m\sqrt{1+m^{2}}}|=\sqrt{2}
\Rightarrow m^{4}+m^{2}=2
\Rightarrow m^{4}+m^{2}-2=0
\Rightarrow (m^{2}-1)(m^{2}+2)=0
\Rightarrow m=\pm 1,m^{2}=-2 (m2 =-2 rejected)
So , tangenth are y=x+2, y=-x-2, THey interset at (-2,0)

Equation of chord PQ is, -2x=2
\Rightarrow x=-1
Equation of chord RS is O =4(x-2)
\Rightarrow x=2
\therefore Coordinates of P,Q,R,S are
P(-1,1), Q(-1,-1),R(2,4),S(2,-4)
Hence , are of PQRS = \frac{(2+8)\times3}{2}=15 sq.units