Consider two straight lines, each of which is tangent
\( \mathrm{P} \) 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
W the ellipse whose center is at the origin \( 0(0,0) \) 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?
(1) For the ellipse, the eccentricity is \( \frac{1}{\sqrt{2}} \) and the length of the latus rectum is 1
(2) For the ellipse, the eccentricity is \( \frac{1}{2} \) and the length of the latus rectum is \( \frac{1}{2} \)
(4) The area of the region bounded by the ellipse between the lines \( x=\frac{1}{\sqrt{2}} \) and \( x=1 \) is \( \frac{(\pi-2)}{16} \)
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