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在直角坐标系
xOy中,曲线
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的参数方程为
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(
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为参数).在以
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为极点,
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轴正半轴为极轴的极坐标系中,直线

的极坐标方程为
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.
(1)求曲线
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的普通方程和直线

的直角坐标方程;
(2)设点
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,若直线

与曲线
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交于
A,B两点,求三角形
POA和三角形
POB面积乘积
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的值.
已知函数
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,若
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的最小值为0,
(1)求
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的值;
(2)若
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,证明:
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存在唯一的极大值点
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,且
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.
如图,四棱锥
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,侧面
PAD是边长为2的正三角形且与底面垂直,底面
ABCD是
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的菱形,
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为棱
PC上的动点且
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.
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(1)求证:
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为直角三角形;
(2)试确定
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的值,使得三棱锥
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的体积为
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.
已知椭圆
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的左、右焦点分别为
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,点
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是椭圆上一点,若
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的内心为
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,连接
PM并延长交
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轴于点
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,且
_____________.
已知数列
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为各项均不相等的等比数列,其前
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项和为
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,且
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成等差数列,则
_____________.
某几何体的三视图如图所示,则该几何体的表面积为
_____________.

已知向量
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的夹角为
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,若
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,则
_____________.
已知
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分别是双曲线
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的左、右焦点,过

作双曲线

的渐近线

的垂线,垂足为
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,且与双曲线

的左支交于点
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,若
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(
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为坐标原点),则双曲线的离心率为(
)
已知函数
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,将
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图象上所有的点的横坐标缩短到原来的
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(纵坐标不变)得到函数
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的图象,若
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在
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上恰有一个极值点,则

的取值不可能是(
)
设
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,直线
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与直线
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相交于点

,点

是圆
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上的一个动点,则
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的最小值为(
).