Consider two straight lines, each of which is tangent to both the circle `x^2+y^2=1/2` and the parabola `y^2=4x` . Let these lines intersect at the point `Q` . Consider the ellipse whose center is at the origin `O(0,\ 0)` and whose semi-major axis is `O Q` . If the length of the minor axis of this ellipse is `sqrt(2)` , then which of the following statement(s) is (are) TRUE? For the ellipse, the eccentricity is `1/(sqrt(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/(sqrt(2))` and `x=1` is `1/(4sqrt(2))(pi-2)` (d) The area of the region bounded by the ellipse between the lines `x=1/(sqrt(2))` and `x=1` is `1/(16)(pi-2)`

Options

A. For the ellipse, the eccentricity is `1/sqrt2` 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 bouded by the ellipse between the lines `x =1/sqrt2` and x=1 is `1/4sqrt2(pi-2)`
D. The area of the region bounded by the ellipse between the lines `x=1/sqrt2` and x =1 is `1/16 (pi-2)`

Answer

A, C