1, tan∠AOE=4/3, that is, Y/X=4/3, that is, the coordinate of point a is (3,4), and the inverse proportional function Y=K/X, K=YX= 12.

So the inverse proportional function is y =12/x.

2. The coordinate of point B is (-6, n), and it is substituted into the inverse proportional function: n =-12/6 =-2 = y. 。

Make an extension line perpendicular to the X axis (E) from point A, and an extension line perpendicular to the Y axis (F) from point B to intersect with point D.. have

△ABD = 1/2 *(Xa-Xb)*(Ya-Yb)=(3+6)*(4+2)/2 = 27。

△AOF= 1/2*4*3=6

△ABD= 1/2*2*6=6

□OFDE=3*2=6

△AOB =△ABD-△AOF-△ABD-□OFDE = 27-6-6-6 = 9

That is, the area of δ δ△AOB is 9.