Consider two straight lines, each of which is tangent to both the circle x^2+y^2=1/2 and the para...

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Consider two straight lines, each of which is tangent to both the circle x^2+y^2=1/2 and the parabola y^2=4 x. Let these lines intersect at the point Q. Consider the ellipse whose centre is at the origin O(0,0) and whose semi-major is OQ. If the length of the minor axis of this ellipse is √(2), then which of the following statement(s) is(are) TRUE ?
(A) For the ellipse, the eccentricity is 1/√(2) and the length of the latus rectum is 1
(B) For the ellipse, the eccentricity is 1/2 and the length of the latus rectum is 1/2
(C) The area of the region bounded by the ellipse between the lines x=1/√(2) and x=1 is 1/4 √(2)(π-2)
(D) The area of the region bounded by the ellipse between the lines x=1/√(2) and x=1 is 1/16(π-2)

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