WV these lines intersect at the point \( Q \). Consider the ellipse whose center is at the origi...

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WV 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 elipse is \( \sqrt{2} \), then the which of the following statement \( (s) \) is (are) TRUE ?
[JEE Advanced-2018]
(a) For the ellipse, the eccentricity is \( \frac{1}{\sqrt{2}} \) and the length of the latus rectrum 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 \( \frac{1}{4 \sqrt{2}}(\pi-2) \)
(d) The area of the region bounded by the ellipse between the lines \( x=\frac{1}{\sqrt{2}} \) and \( x=1 \) is \( \frac{1}{16}(\pi-2) \)
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