a(x-2)-2y+4=0
所以,當x=2時,y=2
即直l1過定點(2,2)
由l2:2x+a^2y=2a^2+4變形得
a^2(y-2)+2x-4=0
所以當y=2時,x=2
即直線l2過定點(2,2)
(2)如圖:
(3)直線l1與y軸交點為A(0,2-a),
直線l2與x軸交點為B(a^2+2,0),如圖
由直線l1:ax-2y-2a+4=0知,直線l1也過定點C(2,2)
過C點作x軸垂線,垂足為D,
于是S四邊形AOBC=S梯形AODC+S△BCD
=1/2(2-a+2)*2+1/2a^2 *2
=a^2-a+4
=a^2-a+(1/2)^2-(1/2)^2+4
=(a-1/2)^2+15/4
∴當a=1/2時,S四過形AOBC最?。?br/>此時S四邊形AOBC=15/4
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