题干

如图所示,在△ABC中,AB的中点为O,且OA=1,点D在AB的延长线上,且 BD=
1
2
AB
.固定边AB,在平面内移动顶点C,使得圆M与边BC,边AC的延长线相切,并始终与AB的延长线相切于点D,记顶点C的轨迹为曲线Γ.以AB所在直线为x轴,O为坐标原点如图所示建立平面直角坐标系.

(Ⅰ)求曲线Γ的方程;

(Ⅱ)设动直线l交曲线Γ于E、F两点,且以EF为直径的圆经过点O,求△OEF面积的取值范围.

上一题 下一题 0.0难度 选择题 更新时间:2018-06-19 02:40:56

答案(点此获取答案解析)

解:(Ⅰ)依题意得AB=2,BD=1,设动圆M与边AC的延长线相切于T1,与边BC相切于T2,则AD=AT1,BD=BT2,CT1=CT2

所以AD+BD=AT1+BT2=AC+CT1+BT2=AC+CT1+CT2=AC+BC=AB+2BD=

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语法填空

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