Ellipse

Let C be the circle of minimum area enclosing the ellipse E:‌

x2

a2

+‌

y2

b2

=1 with eccentricity ‌

1

2

and foci (±2,0). Let PQR be a variable triangle, whose vertex P is on the circle C and the side QR of length 2a is parallel to the major axis of E and contains the point of intersection of E with the negative y-axis. Then the maximum area of the triangle PQR is: