问题 填空题
已知定点A(2,0),点P(x,y)的坐标满足
x-4y+3≤0
3x+5y-25≤0
x-a≥0
,当
OP
OA
|
OA
|
(O为坐标原点)的最小值是2时,实数a的值是______.
答案

作出不等式组对应的平面区域如图:(阴影部分)

∵定点A(2,0),点P(x,y),

OP
=(x,y),
OA
=(2,0),

z=

OP
OA
|
OA
|
=
2x
2
=x,

要使当

OP
OA
|
OA
|
(O为坐标原点)的最小值是2时,即x=2时,点P落在直线x=a上,

此时a=2.

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