Question

已知：如图，在平面直角坐标系xOy中，直线与轴交于点A (– 2，0)，与反比例函数在第一象限内的图象交于点B (2，n)，连结BO，若．

（1）求该反比例函数的解析式和直线的解析式；
（2）若直线AB与轴的交点为C，求△OCB的面积．

Answer 1

（1） ；
（2）解析:
解：(1) 由，得．
∵点在第一象限内，．
∴．∴．····················································· （2分）
∴点的坐标是．······················································· （3分）
设该反比例函数的解析式为．
将点的坐标代入，得，∴．································ （4分）
∴反比例函数的解析式为：．·········································· （5分）
设直线的解析式为．
将点，的坐标分别代入，得···························· （6分）
解得 ···································································· （7分）
∴直线的解析式为．············································ （8分）
(2) 在中，令，得．
∴点的坐标是．∴．······································· （9分）
∴．········································ （10分）