Consider two straight lines, each of which is tangent to both the circle $x^2+y^2=\frac{1}{2}$and the parabola $y^2=4x$. Let these lines intersect at the point $Q$. Consider the ellipse whose center is at the origin $O\left(0,0\right)$and whose semi-major axis is $OQ$. 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 $\frac{1}{\sqrt{2}}$and the length of the latus rectum is 1(b) For the ellipse, the eccentricity is $\frac{1}{2}$and the length of the latus rectum is $\frac{1}{2}$(c) The area of the region bounded by the ellipse between the lines $x=\frac{1}{\sqrt{2}}$and $x=1$is $\frac{1}{4\sqrt{2}}\left(\pi -2\right)$(d) The area of the region bounded by the ellipse between the lines $x=\frac{1}{\sqrt{2}}$and $x=1$is $\frac{1}{16}\left(\pi -2\right)$

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