Question

（7分）如图，正比例函数的图象与反比例函数在第一象限
的图象交于点，过点作轴的垂线，垂足为，已知的面积为1.
（1）求反比例函数的解析式；
（2）如果为反比例函数在第一象限图象上的点（点与点不重合），且点的横坐标为1，在轴上求一点，使最小.

Answer 1

解：（1）设点的坐标为（，），则.∴.
∵,∴.∴.
∴反比例函数的解析式为.··································································· 3分
(2) 由 得 ∴为（，）. ·············································· 4分
设点关于轴的对称点为，则点的坐标为（，）.
令直线的解析式为.
∵为（，）∴∴
∴的解析式为.···································································· 6分
当时，.∴点为（，）. ······················································ 7分解析:
略