<Qua-2025-763>, hint

By coordinate system, Let B(0,0) , C(2,0), A(0,2), Then  N(1,2)

P(0,4)  E(-1,1)  M(0, 2/3)  F(-2,-2). Since BM/BC=-1/3 slope of CQ is -3/4

(tan2x=2tanx/(1-tan^x))

CQ; y=-3/4(x-2) and Q(-2/3, 2). Hence Slope of QM=-2, slope of FC=1/2