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题型:解答题 难度系数:0.65 引用次数:3090 更新时间:2018/06/11 03:12:00 题号:6505579
设椭圆 (a>b>0)的左焦点为F,上顶点为B. 已知椭圆的离心率为,点A的坐标为,且.
(I)求椭圆的方程;
(II)设直线l与椭圆在第一象限的交点为P,且l与直线AB交于点Q. 若 (O为原点) ,求k的值.

【知识点】

圆锥曲线综合 解读
类题推荐
【推荐1】 设椭圆eqId18cc1825557e4737b9bd0d8b23a98939的左焦点为eqIdd5b10b2a13f148b78e0d5a1b820538fd,左顶点为eqIdcc614bd3390c4d028df189b234dcc351,上顶点为B.已知eqIde01e82a8bb4a4dcebd1349b4ce72d485eqIdaad7b72a25924d078d2360cdc99f1090为原点).
(Ⅰ)求椭圆的离心率;
(Ⅱ)设经过点eqIdd5b10b2a13f148b78e0d5a1b820538fd且斜率为eqIddda48cced83d424b89b7d8f8c62b1056的直线eqId417e80f1349244878d01fe90e0891f5f与椭圆在eqIdc12aac8c2448479687a40735b3572a23轴上方的交点为eqIdd7be5abad1e34f6db17a56660de8d54f,圆eqId19a4eb16029e4550a14f2afe4741a3c3同时与eqIdc12aac8c2448479687a40735b3572a23轴和直线eqId417e80f1349244878d01fe90e0891f5f相切,圆心eqId19a4eb16029e4550a14f2afe4741a3c3在直线eqIdd59777a92d8f4da290823fc3dc6b5c26上,且eqId6aa424171038462eafa609093f1d3686,求椭圆的方程.
难度系数:0.4使用:308次题型:解答题更新:2019/6/9
【推荐2】已知曲线eqIdb44ee8c586a44804a65e7dbd7f39c453,为直线eqId8f30f709ef4647f082c6f0000a1d1736上的动点,过eqId0cd8063abf2b458f80091bc51b75a904eqId19a4eb16029e4550a14f2afe4741a3c3的两条切线,切点分别为eqIdb1303264010b459d9f702b468b17ec1f.
(1)证明:直线eqId99a3187c2b8f4bcc9703c74c3b72f1f3过定点:
(2)若以eqId7dfb680270784f1eab0c846f7280da3d为圆心的圆与直线eqId99a3187c2b8f4bcc9703c74c3b72f1f3相切,且切点为线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3的中点,求该圆的方程.
难度系数:0.4使用:656次题型:解答题更新:2019/6/9
【推荐3】已知椭圆eqIdfd8674e21002436f9476310a52d934ec的左、右焦点为eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e,长轴端点为eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5ceqIdaad7b72a25924d078d2360cdc99f1090为椭圆中心,eqId4db1ace58ea04db6a776c62ec67c8e9c,斜率为eqId5f816d038c584dc7a249120298677ef3的直线eqId417e80f1349244878d01fe90e0891f5f与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3交于不同的两点,这两点在eqIdc12aac8c2448479687a40735b3572a23轴上的射影恰好是椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的两个焦点.
figure
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)若抛物线eqIdd050af449075401299cc78c647d310e8上存在两个点eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6,椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上存在两个点eqIdd7be5abad1e34f6db17a56660de8d54feqIdca9308a4ebd84ed8a28d8a519a8dbb39,满足eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6eqIdde963a24921f4ee7a991bf9d4f43a42e三点共线,eqIdd7be5abad1e34f6db17a56660de8d54feqIdca9308a4ebd84ed8a28d8a519a8dbb39eqIdde963a24921f4ee7a991bf9d4f43a42e三点共线,且eqId732aae6386de4962a582f29411686329,求四边形eqId4c30f3f9c9574605ac9074dd045ebfa1面积的最小值.
难度系数:0.4使用:8次题型:解答题更新:2019/6/27
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