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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阅读理解

    In the 1600's when the Spanish moved into what later was to become the southwestern United States, they came across the ancestors of the modern-day Pueblo, Hopi, and Zuni peoples. These ancestors, known variously as the basket makers, the Ancient ones, had lived in the area for at least 2000 years. They were an advanced agricultura people who used irrigation to help grow their drops.

    The Anasazi lived in houses constructed of earth and wood. Anasazi houses were originally built underground and were entered from the roof. But around the year 700 A. D., the Anasazi began to build their homes above ground and join them together into multistoried complexes, which the Spanish called villages. Separate underground rooms in these villages—known as kivas or holy places—were set aside for religious ceremonies. Each kiva had a fireplace and a hole that was believed to lead to the underworld. The largest villages had five stories and more than 800 rooms.

    The Anasazi family was ruled by women. The sacred objects of the family were under the control of the oldest female, but the actual ceremonies were conducted by her brother or son. Women owned the rooms in the village and the crops, once they were harvested. While still growing, crops belonged to the men who, in contrast to most other Native American groups, planted them. The women made baskets and pottery; the men wove cloth and made jewelry.

    Each village had two chiefs. The village chief dealt with land arguments and religious affairs. The war chief led the men in fighting during occasional conflicts that broke out with neithboring villages and directed the men in commnity building projects. The political and social organization of the Anasazi made it almost impossible for outer groups to conquer them.

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