已知直线y=-3/4x+6与x轴交于点B,与y轴交于点A.①圆P经过点OAB,试求P点坐标.②点Q为线段AB上一点,

(1)
A(0,6),B(8,0)
OA,OB的中垂线分别为y = 3,x = 4,交点为P(4,3)
半径r = OP = 5
(2)
Q(q,-3q/4 + 6)
S = (1/2)ON*NQ = (1/2)q(6 - 3q/4) = -(3/8)(q -4)² + 6
面积的最大值为6
(3)
角OAB的平分线为y = 6 - 2x
E(e,6 - 2e)
e = (2/3)(6 - 2e)
e = 12/7
E(12/7,18/7)