In triangle \( A B C, a=4 \) and \( b=c=2 \sqrt{2} \). A point \( P \) moves within the triangle...

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In triangle \( A B C, a=4 \) and \( b=c=2 \sqrt{2} \). A point \( P \) moves within the triangle such that the square of its distance from \( B C \) is half the area of rectangle contained by its distances from the other two sides. If \( D \) be the centre of locus of then
(a) Locus of \( P \) is an ellipse with eccentricity \( \sqrt{\frac{2}{3}} \)
(b) Locus of \( P \) is a hyperbola with eccentricity \( \sqrt{\frac{3}{2}} \)
(c) Area of the quadrilateral \( A B C D=\frac{16}{3} \) sq. units
(d) Area of the quadrilateral \( A B C D=\frac{32}{3} \) sq. units
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