The line x3+y4=1meets the y and x-axis at A and B, respectively. A square ABCD is constructed on the line segment AB away from the origin. The coordinates of the vertex of the square farthest from the origin are

The coordinates of A are (0, 4) and those of B are (3, 0). BC=AB=32+42=5In △BCL  ∠CBL=180-90-θ=90-θsin(90-θ)=CLBCcos θ= CLBC and CL=BCcos⁡θcos(90-θ)=BLBCor  BL=BCsin⁡θ or  BL=5×45=4 and CL=5×35=3 Similarly, MD=4 and AM=3 . So, the coordinates of C are (OB+BL,CL)≡(7,3) and those of D are (MD,OA+AM)≡4,7The coordinates of the vertex farthest from the origin are (4,7).