Pair of straight lines through \( A(1,1) \) are drawn to intersect the line \( 2 x+4 y=5 \) at \...

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Pair of straight lines through \( A(1,1) \) are drawn to intersect the line \( 2 x+4 y=5 \) at \( B \) and \( C \). If angle between the pair of straight line is \( \frac{\pi}{3} \), then the locus of incentre of \( \triangle A B C \) is
(A) \( 11 x^{2}-y^{2}-16 x y-10 x+10 y-5=0 \)
(B) \( 11 y^{2}-x^{2}+16 x y-10 y+20=0 \)
(C) \( 11 x^{2}+y^{2}-16 x y-10 x+10 y+5=0 \)
(D) \( 11 y^{2}-x^{2}+16 x y-10 x-30 y+15=0 \)
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